{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 0
   },
   "source": [
    "# Transformer\n",
    ":label:`sec_transformer`\n",
    "\n",
    "我们在 :numref:`subsec_cnn-rnn-self-attention`中比较了卷积神经网络（CNN）、循环神经网络（RNN）和自注意力（self-attention）。值得注意的是，自注意力同时具有并行计算和最短的最大路径长度这两个优势。因此，使用自注意力来设计深度架构是很有吸引力的。对比之前仍然依赖循环神经网络实现输入表示的自注意力模型 :cite:`Cheng.Dong.Lapata.2016,Lin.Feng.Santos.ea.2017,Paulus.Xiong.Socher.2017`，transformer模型完全基于注意力机制，没有任何卷积层或循环神经网络层 :cite:`Vaswani.Shazeer.Parmar.ea.2017`。尽管transformer最初是应用于在文本数据上的序列到序列学习，但现在已经推广到各种现代的深度学习中，例如语言、视觉、语音和强化学习领域。\n",
    "\n",
    "## 模型\n",
    "\n",
    "Transformer作为编码器－解码器架构的一个实例，其整体架构图在 :numref:`fig_transformer`中展示。正如所见到的，transformer是由编码器和解码器组成的。与 :numref:`fig_s2s_attention_details`中基于Bahdanau注意力实现的序列到序列的学习相比，transformer的编码器和解码器是基于自注意力的模块叠加而成的，源（输入）序列和目标（输出）序列的*嵌入*（embedding）表示将加上*位置编码*（positional encoding），再分别输入到编码器和解码器中。\n",
    "\n",
    "![transformer架构](../img/transformer.svg)\n",
    ":width:`500px`\n",
    ":label:`fig_transformer`\n",
    "\n",
    "图 :numref:`fig_transformer`中概述了transformer的架构。从宏观角度来看，transformer的编码器是由多个相同的层叠加而成的，每个层都有两个子层（子层表示为$\\mathrm{sublayer}$）。第一个子层是*多头自注意力*（multi-head self-attention）汇聚；第二个子层是*基于位置的前馈网络*（positionwise feed-forward network）。具体来说，在计算编码器的自注意力时，查询、键和值都来自前一个编码器层的输出。受 :numref:`sec_resnet`中残差网络的启发，每个子层都采用了*残差连接*（residual connection）。在transformer中，对于序列中任何位置的任何输入$\\mathbf{x} \\in \\mathbb{R}^d$，都要求满足$\\mathrm{sublayer}(\\mathbf{x}) \\in \\mathbb{R}^d$，以便残差连接满足$\\mathbf{x} + \\mathrm{sublayer}(\\mathbf{x}) \\in \\mathbb{R}^d$。在残差连接的加法计算之后，紧接着应用*层规范化*（layer normalization） :cite:`Ba.Kiros.Hinton.2016`。因此，输入序列对应的每个位置，transformer编码器都将输出一个$d$维表示向量。\n",
    "\n",
    "Transformer解码器也是由多个相同的层叠加而成的，并且层中使用了残差连接和层规范化。除了编码器中描述的两个子层之外，解码器还在这两个子层之间插入了第三个子层，称为*编码器－解码器注意力*（encoder-decoder attention）层。在编码器－解码器注意力中，查询来自前一个解码器层的输出，而键和值来自整个编码器的输出。在解码器自注意力中，查询、键和值都来自上一个解码器层的输出。但是，解码器中的每个位置只能考虑该位置之前的所有位置。这种*掩蔽*（masked）注意力保留了*自回归*（auto-regressive）属性，确保预测仅依赖于已生成的输出词元。\n",
    "\n",
    "我们已经描述并实现了基于缩放点积多头注意力 :numref:`sec_multihead-attention`和位置编码 :numref:`subsec_positional-encoding`。接下来，我们将实现transformer模型的剩余部分。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "origin_pos": 2,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import pandas as pd\n",
    "import torch\n",
    "from torch import nn\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 4
   },
   "source": [
    "## [**基于位置的前馈网络**]\n",
    "\n",
    "基于位置的前馈网络对序列中的所有位置的表示进行变换时使用的是同一个多层感知机（MLP），这就是称前馈网络是*基于位置的*（positionwise）的原因。在下面的实现中，输入`X`的形状（批量大小，时间步数或序列长度，隐单元数或特征维度）将被一个两层的感知机转换成形状为（批量大小，时间步数，`ffn_num_outputs`）的输出张量。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "origin_pos": 6,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "#@save\n",
    "class PositionWiseFFN(nn.Module):\n",
    "    \"\"\"基于位置的前馈网络\"\"\"\n",
    "    # 说白了就是两个全连接层，是一个mlp\n",
    "    # 对于pytorch来说，如果是多个维度，前面的都算是样本维，只有最后的时feature维度\n",
    "    def __init__(self, ffn_num_input, ffn_num_hiddens, ffn_num_outputs,\n",
    "                 **kwargs):\n",
    "        super(PositionWiseFFN, self).__init__(**kwargs)\n",
    "        self.dense1 = nn.Linear(ffn_num_input, ffn_num_hiddens)\n",
    "        self.relu = nn.ReLU()\n",
    "        self.dense2 = nn.Linear(ffn_num_hiddens, ffn_num_outputs)\n",
    "\n",
    "    def forward(self, X):\n",
    "        return self.dense2(self.relu(self.dense1(X)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 8
   },
   "source": [
    "下面的例子显示，[**改变张量的最里层维度的尺寸**]，会改变成基于位置的前馈网络的输出尺寸。因为用同一个多层感知机对所有位置上的输入进行变换，所以当所有这些位置的输入相同时，它们的输出也是相同的。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "origin_pos": 10,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.7652, -0.1718,  0.1267, -0.4058, -0.0321, -0.1480, -0.6325,  0.4314],\n",
       "        [-0.7652, -0.1718,  0.1267, -0.4058, -0.0321, -0.1480, -0.6325,  0.4314],\n",
       "        [-0.7652, -0.1718,  0.1267, -0.4058, -0.0321, -0.1480, -0.6325,  0.4314]],\n",
       "       grad_fn=<SelectBackward>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ffn = PositionWiseFFN(4, 4, 8)\n",
    "ffn.eval()\n",
    "ffn(torch.ones((2, 3, 4)))[0]\n",
    "# 最后的4会变成8，后面的维度会发生变化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 12
   },
   "source": [
    "## 残差连接和层规范化\n",
    "\n",
    "现在让我们关注 :numref:`fig_transformer`中的“*加法和规范化*（add&norm）”组件。正如在本节开头所述，这是由残差连接和紧随其后的层规范化组成的。两者都是构建有效的深度架构的关键。\n",
    "\n",
    "在 :numref:`sec_batch_norm`中，我们解释了在一个小批量的样本内基于批量规范化对数据进行重新中心化和重新缩放的调整。层规范化和批量规范化的目标相同，但层规范化是基于特征维度进规范化。尽管批量规范化在计算机视觉中被广泛应用，但在自然语言处理任务中（输入通常是变长序列）批量规范化通常不如层规范化的效果好。\n",
    "\n",
    "以下代码[**对比不同维度的层规范化和批量规范化的效果**]。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "origin_pos": 14,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "layer norm: tensor([[-1.0000,  1.0000],\n",
      "        [-1.0000,  1.0000]], grad_fn=<NativeLayerNormBackward>) \n",
      "batch norm: tensor([[-1.0000, -1.0000],\n",
      "        [ 1.0000,  1.0000]], grad_fn=<NativeBatchNormBackward>)\n"
     ]
    }
   ],
   "source": [
    "ln = nn.LayerNorm(2)\n",
    "bn = nn.BatchNorm1d(2)\n",
    "X = torch.tensor([[1, 2], [2, 3]], dtype=torch.float32)\n",
    "# 在训练模式下计算X的均值和方差\n",
    "print('layer norm:', ln(X), '\\nbatch norm:', bn(X))\n",
    "'''\n",
    "layernorm 每个样本变成均值为0，方差为1\n",
    "batchnorm 每个特征变成均值为0，方差为1\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 16
   },
   "source": [
    "现在我们可以[**使用残差连接和层规范化**]来实现`AddNorm`类。暂退法也被作为正则化方法使用。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "origin_pos": 18,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "#@save\n",
    "class AddNorm(nn.Module):\n",
    "    \"\"\"残差连接后进行层规范化\"\"\"\n",
    "    def __init__(self, normalized_shape, dropout, **kwargs):\n",
    "        super(AddNorm, self).__init__(**kwargs)\n",
    "        self.dropout = nn.Dropout(dropout)\n",
    "        self.ln = nn.LayerNorm(normalized_shape)\n",
    "\n",
    "    def forward(self, X, Y):\n",
    "        '''\n",
    "        @para X：原来的输入\n",
    "        @para y：输出\n",
    "        '''\n",
    "        return self.ln(self.dropout(Y) + X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 20
   },
   "source": [
    "残差连接要求两个输入的形状相同，以便[**加法操作后输出张量的形状相同**]。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "origin_pos": 22,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 3, 4])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 残差连接要求两个输入的形状相同\n",
    "add_norm = AddNorm([3, 4], 0.5)\n",
    "add_norm.eval()\n",
    "add_norm(torch.ones((2, 3, 4)), torch.ones((2, 3, 4))).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 24
   },
   "source": [
    "## 编码器\n",
    "\n",
    "有了组成transformer编码器的基础组件，现在可以先[**实现编码器中的一个层**]。下面的`EncoderBlock`类包含两个子层：多头自注意力和基于位置的前馈网络，这两个子层都使用了残差连接和紧随的层规范化。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "origin_pos": 26,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "#@save\n",
    "class EncoderBlock(nn.Module):\n",
    "    \"\"\"transformer编码器块\"\"\"\n",
    "    def __init__(self, key_size, query_size, value_size, num_hiddens,\n",
    "                 norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,\n",
    "                 dropout, use_bias=False, **kwargs):\n",
    "        super(EncoderBlock, self).__init__(**kwargs)\n",
    "        # 多头注意力\n",
    "        self.attention = d2l.MultiHeadAttention(\n",
    "            key_size, query_size, value_size, num_hiddens, num_heads, dropout,\n",
    "            use_bias)\n",
    "        # addnorm\n",
    "        self.addnorm1 = AddNorm(norm_shape, dropout)\n",
    "        # ffn\n",
    "        self.ffn = PositionWiseFFN(\n",
    "            ffn_num_input, ffn_num_hiddens, num_hiddens)\n",
    "        # addnorm\n",
    "        self.addnorm2 = AddNorm(norm_shape, dropout)\n",
    "\n",
    "    def forward(self, X, valid_lens):\n",
    "        '''\n",
    "        encoder一层，包括一个多头注意力，一个ffn，两个add&norm\n",
    "        '''\n",
    "        Y = self.addnorm1(\n",
    "            X, \n",
    "            self.attention(X, X, X, valid_lens))\n",
    "        return self.addnorm2(Y, self.ffn(Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 28
   },
   "source": [
    "正如我们所看到的，[**transformer编码器中的任何层都不会改变其输入的形状**]。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "origin_pos": 30,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 100, 24])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# batchsize为2，sequence长度为100，维度为24.输入是他，输出之后，维度没有变化\n",
    "X = torch.ones((2, 100, 24))\n",
    "valid_lens = torch.tensor([3, 2])\n",
    "encoder_blk = EncoderBlock(24, 24, 24, 24, [100, 24], 24, 48, 8, 0.5)\n",
    "encoder_blk.eval()\n",
    "encoder_blk(X, valid_lens).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 32
   },
   "source": [
    "在实现下面的[**transformer编码器**]的代码中，我们堆叠了`num_layers`个`EncoderBlock`类的实例。由于我们使用的是值范围在$-1$和$1$之间的固定位置编码，因此通过学习得到的输入的嵌入表示的值需要先乘以嵌入维度的平方根进行重新缩放，然后再与位置编码相加。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "origin_pos": 34,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "#@save\n",
    "class TransformerEncoder(d2l.Encoder):\n",
    "    \"\"\"transformer编码器\"\"\"\n",
    "    def __init__(self, vocab_size, key_size, query_size, value_size,\n",
    "                 num_hiddens, norm_shape, ffn_num_input, ffn_num_hiddens,\n",
    "                 num_heads, num_layers, dropout, use_bias=False, **kwargs):\n",
    "        super(TransformerEncoder, self).__init__(**kwargs)\n",
    "        self.num_hiddens = num_hiddens\n",
    "        self.embedding = nn.Embedding(vocab_size, num_hiddens)\n",
    "        self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)\n",
    "        self.blks = nn.Sequential() #多层网络\n",
    "        for i in range(num_layers):\n",
    "            self.blks.add_module(\"block\"+str(i),\n",
    "                EncoderBlock(key_size, query_size, value_size, num_hiddens,\n",
    "                             norm_shape, ffn_num_input, ffn_num_hiddens,\n",
    "                             num_heads, dropout, use_bias))\n",
    "\n",
    "    def forward(self, X, valid_lens, *args):\n",
    "        # 因为位置编码值在-1和1之间，\n",
    "        # 因此嵌入值乘以嵌入维度的平方根进行缩放，\n",
    "        # 然后再与位置编码相加。\n",
    "        X = self.pos_encoding(\n",
    "            self.embedding(X) * math.sqrt(self.num_hiddens)) # 控制大小\n",
    "        self.attention_weights = [None] * len(self.blks)\n",
    "        # 输入到n层encoder\n",
    "        for i, blk in enumerate(self.blks):\n",
    "            X = blk(X, valid_lens)\n",
    "            self.attention_weights[\n",
    "                i] = blk.attention.attention.attention_weights\n",
    "        return X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 36
   },
   "source": [
    "下面我们指定了超参数来[**创建一个两层的transformer编码器**]。\n",
    "Transformer编码器输出的形状是（批量大小，时间步数目，`num_hiddens`）。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "origin_pos": 38,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 100, 24])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "encoder = TransformerEncoder(\n",
    "    200, 24, 24, 24, 24, [100, 24], 24, 48, 8, 2, 0.5)\n",
    "encoder.eval()\n",
    "encoder(torch.ones((2, 100), dtype=torch.long), valid_lens).shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 40
   },
   "source": [
    "## 解码器\n",
    "\n",
    "如 :numref:`fig_transformer`所示，[**transformer解码器也是由多个相同的层组成**]。在`DecoderBlock`类中实现的每个层包含了三个子层：解码器自注意力、“编码器-解码器”注意力和基于位置的前馈网络。这些子层也都被残差连接和紧随的层规范化围绕。\n",
    "\n",
    "正如在本节前面所述，在掩蔽多头解码器自注意力层（第一个子层）中，查询、键和值都来自上一个解码器层的输出。关于*序列到序列模型*（sequence-to-sequence model），在训练阶段，其输出序列的所有位置（时间步）的词元都是已知的；然而，在预测阶段，其输出序列的词元是逐个生成的。因此，在任何解码器时间步中，只有生成的词元才能用于解码器的自注意力计算中。为了在解码器中保留自回归的属性，其掩蔽自注意力设定了参数`dec_valid_lens`，以便任何查询都只会与解码器中所有已经生成词元的位置（即直到该查询位置为止）进行注意力计算。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "origin_pos": 42,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class DecoderBlock(nn.Module):\n",
    "    \"\"\"解码器中第i个块\"\"\"\n",
    "    def __init__(self, key_size, query_size, value_size, num_hiddens,\n",
    "                 norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,\n",
    "                 dropout, i, **kwargs):\n",
    "        super(DecoderBlock, self).__init__(**kwargs)\n",
    "        self.i = i #记下i\n",
    "        \n",
    "        self.attention1 = d2l.MultiHeadAttention(\n",
    "            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n",
    "        self.addnorm1 = AddNorm(norm_shape, dropout)\n",
    "        \n",
    "        self.attention2 = d2l.MultiHeadAttention(\n",
    "            key_size, query_size, value_size, num_hiddens, num_heads, dropout)\n",
    "        self.addnorm2 = AddNorm(norm_shape, dropout)\n",
    "        \n",
    "        self.ffn = PositionWiseFFN(ffn_num_input, ffn_num_hiddens,\n",
    "                                   num_hiddens)\n",
    "        self.addnorm3 = AddNorm(norm_shape, dropout)\n",
    "\n",
    "    def forward(self, X, state):\n",
    "        enc_outputs, enc_valid_lens = state[0], state[1]\n",
    "        # 训练阶段，输出序列的所有词元都在同一时间处理，\n",
    "        # 因此state[2][self.i]初始化为None。\n",
    "        # 预测阶段，输出序列是通过词元一个接着一个解码的，\n",
    "        # 因此state[2][self.i]包含着直到当前时间步第i个块解码的输出表示\n",
    "        if state[2][self.i] is None:\n",
    "            key_values = X #train\n",
    "        else:\n",
    "            key_values = torch.cat((state[2][self.i], X), axis=1) #prediction，存前面的输出\n",
    "        \n",
    "        state[2][self.i] = key_values\n",
    "        \n",
    "        if self.training: # train的时候把后面的输出遮掉\n",
    "            batch_size, num_steps, _ = X.shape\n",
    "            # dec_valid_lens的开头:(batch_size,num_steps),\n",
    "            # 其中每一行是[1,2,...,num_steps]\n",
    "            dec_valid_lens = torch.arange(\n",
    "                1, num_steps + 1, device=X.device).repeat(batch_size, 1)\n",
    "        else:\n",
    "            dec_valid_lens = None\n",
    "\n",
    "        # 自注意力\n",
    "        X2 = self.attention1(X, key_values, key_values, dec_valid_lens)\n",
    "        Y = self.addnorm1(X, X2)\n",
    "        # 编码器－解码器注意力。\n",
    "        # enc_outputs的开头:(batch_size,num_steps,num_hiddens)\n",
    "        Y2 = self.attention2(Y, enc_outputs, enc_outputs, enc_valid_lens)\n",
    "        Z = self.addnorm2(Y, Y2)\n",
    "        \n",
    "        return self.addnorm3(Z, self.ffn(Z)), state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 44
   },
   "source": [
    "为了便于在“编码器－解码器”注意力中进行缩放点积计算和残差连接中进行加法计算，[**编码器和解码器的特征维度都是`num_hiddens`。**]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "origin_pos": 46,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 100, 24])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decoder_blk = DecoderBlock(24, 24, 24, 24, [100, 24], 24, 48, 8, 0.5, 0)\n",
    "decoder_blk.eval()\n",
    "X = torch.ones((2, 100, 24))\n",
    "state = [encoder_blk(X, valid_lens), valid_lens, [None]]\n",
    "decoder_blk(X, state)[0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 48
   },
   "source": [
    "现在我们构建了由`num_layers`个`DecoderBlock`实例组成的完整的[**transformer解码器**]。最后，通过一个全连接层计算所有`vocab_size`个可能的输出词元的预测值。解码器的自注意力权重和编码器解码器注意力权重都被存储下来，方便日后可视化的需要。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "origin_pos": 50,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [],
   "source": [
    "class TransformerDecoder(d2l.AttentionDecoder):\n",
    "    '''\n",
    "    与encoder一样\n",
    "    '''\n",
    "    def __init__(self, vocab_size, key_size, query_size, value_size,\n",
    "                 num_hiddens, norm_shape, ffn_num_input, ffn_num_hiddens,\n",
    "                 num_heads, num_layers, dropout, **kwargs):\n",
    "        super(TransformerDecoder, self).__init__(**kwargs)\n",
    "        self.num_hiddens = num_hiddens\n",
    "        self.num_layers = num_layers\n",
    "        self.embedding = nn.Embedding(vocab_size, num_hiddens)\n",
    "        self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)\n",
    "        self.blks = nn.Sequential()\n",
    "        for i in range(num_layers):\n",
    "            self.blks.add_module(\"block\"+str(i),\n",
    "                DecoderBlock(key_size, query_size, value_size, num_hiddens,\n",
    "                             norm_shape, ffn_num_input, ffn_num_hiddens,\n",
    "                             num_heads, dropout, i))\n",
    "        # 输出，做英语法语翻译\n",
    "        self.dense = nn.Linear(num_hiddens, vocab_size)\n",
    "\n",
    "    def init_state(self, enc_outputs, enc_valid_lens, *args):\n",
    "        '''\n",
    "        存状态，最后一维是预测的时候用来存输出用的\n",
    "        '''\n",
    "        return [enc_outputs, enc_valid_lens, [None] * self.num_layers]\n",
    "\n",
    "    def forward(self, X, state):\n",
    "        \n",
    "        X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))\n",
    "        \n",
    "        self._attention_weights = [[None] * len(self.blks) for _ in range (2)]\n",
    "        \n",
    "        for i, blk in enumerate(self.blks):\n",
    "            X, state = blk(X, state)\n",
    "            # 解码器自注意力权重\n",
    "            self._attention_weights[0][\n",
    "                i] = blk.attention1.attention.attention_weights\n",
    "            # “编码器－解码器”自注意力权重\n",
    "            self._attention_weights[1][\n",
    "                i] = blk.attention2.attention.attention_weights\n",
    "        return self.dense(X), state\n",
    "\n",
    "    @property\n",
    "    def attention_weights(self):\n",
    "        return self._attention_weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 52
   },
   "source": [
    "## [**训练**]\n",
    "\n",
    "依照transformer架构来实例化编码器－解码器模型。在这里，指定transformer的编码器和解码器都是2层，都使用4头注意力。与 :numref:`sec_seq2seq_training`类似，为了进行序列到序列的学习，我们在“英语－法语”机器翻译数据集上训练transformer模型。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "origin_pos": 54,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss 0.033, 5089.5 tokens/sec on cuda:0\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"180.65625pt\" version=\"1.1\" viewBox=\"0 0 262.1875 180.65625\" width=\"262.1875pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2021-12-08T21:38:44.026110</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.3.3, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 180.65625 \n",
       "L 262.1875 180.65625 \n",
       "L 262.1875 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 50.14375 143.1 \n",
       "L 245.44375 143.1 \n",
       "L 245.44375 7.2 \n",
       "L 50.14375 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <path clip-path=\"url(#p35e391b3b5)\" d=\"M 91.259539 143.1 \n",
       "L 91.259539 7.2 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_2\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"maa081d2d25\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"91.259539\" xlink:href=\"#maa081d2d25\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 50 -->\n",
       "      <g transform=\"translate(84.897039 157.698438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "        <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <path clip-path=\"url(#p35e391b3b5)\" d=\"M 142.654276 143.1 \n",
       "L 142.654276 7.2 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"142.654276\" xlink:href=\"#maa081d2d25\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 100 -->\n",
       "      <g transform=\"translate(133.110526 157.698438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <path clip-path=\"url(#p35e391b3b5)\" d=\"M 194.049013 143.1 \n",
       "L 194.049013 7.2 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"194.049013\" xlink:href=\"#maa081d2d25\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 150 -->\n",
       "      <g transform=\"translate(184.505263 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <path clip-path=\"url(#p35e391b3b5)\" d=\"M 245.44375 143.1 \n",
       "L 245.44375 7.2 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"245.44375\" xlink:href=\"#maa081d2d25\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 200 -->\n",
       "      <g transform=\"translate(235.9 157.698438)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_5\">\n",
       "     <!-- epoch -->\n",
       "     <g transform=\"translate(132.565625 171.376563)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "       <path d=\"M 18.109375 8.203125 \n",
       "L 18.109375 -20.796875 \n",
       "L 9.078125 -20.796875 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.390625 \n",
       "Q 20.953125 51.265625 25.265625 53.625 \n",
       "Q 29.59375 56 35.59375 56 \n",
       "Q 45.5625 56 51.78125 48.09375 \n",
       "Q 58.015625 40.1875 58.015625 27.296875 \n",
       "Q 58.015625 14.40625 51.78125 6.484375 \n",
       "Q 45.5625 -1.421875 35.59375 -1.421875 \n",
       "Q 29.59375 -1.421875 25.265625 0.953125 \n",
       "Q 20.953125 3.328125 18.109375 8.203125 \n",
       "z\n",
       "M 48.6875 27.296875 \n",
       "Q 48.6875 37.203125 44.609375 42.84375 \n",
       "Q 40.53125 48.484375 33.40625 48.484375 \n",
       "Q 26.265625 48.484375 22.1875 42.84375 \n",
       "Q 18.109375 37.203125 18.109375 27.296875 \n",
       "Q 18.109375 17.390625 22.1875 11.75 \n",
       "Q 26.265625 6.109375 33.40625 6.109375 \n",
       "Q 40.53125 6.109375 44.609375 11.75 \n",
       "Q 48.6875 17.390625 48.6875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-112\"/>\n",
       "       <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "       <path d=\"M 48.78125 52.59375 \n",
       "L 48.78125 44.1875 \n",
       "Q 44.96875 46.296875 41.140625 47.34375 \n",
       "Q 37.3125 48.390625 33.40625 48.390625 \n",
       "Q 24.65625 48.390625 19.8125 42.84375 \n",
       "Q 14.984375 37.3125 14.984375 27.296875 \n",
       "Q 14.984375 17.28125 19.8125 11.734375 \n",
       "Q 24.65625 6.203125 33.40625 6.203125 \n",
       "Q 37.3125 6.203125 41.140625 7.25 \n",
       "Q 44.96875 8.296875 48.78125 10.40625 \n",
       "L 48.78125 2.09375 \n",
       "Q 45.015625 0.34375 40.984375 -0.53125 \n",
       "Q 36.96875 -1.421875 32.421875 -1.421875 \n",
       "Q 20.0625 -1.421875 12.78125 6.34375 \n",
       "Q 5.515625 14.109375 5.515625 27.296875 \n",
       "Q 5.515625 40.671875 12.859375 48.328125 \n",
       "Q 20.21875 56 33.015625 56 \n",
       "Q 37.15625 56 41.109375 55.140625 \n",
       "Q 45.0625 54.296875 48.78125 52.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-99\"/>\n",
       "       <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 75.984375 \n",
       "L 18.109375 75.984375 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-104\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"61.523438\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"125\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"186.181641\" xlink:href=\"#DejaVuSans-99\"/>\n",
       "      <use x=\"241.162109\" xlink:href=\"#DejaVuSans-104\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <path clip-path=\"url(#p35e391b3b5)\" d=\"M 50.14375 122.55122 \n",
       "L 245.44375 122.55122 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_10\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m4956b7ea0d\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#m4956b7ea0d\" y=\"122.55122\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0.05 -->\n",
       "      <g transform=\"translate(20.878125 126.350439)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <path clip-path=\"url(#p35e391b3b5)\" d=\"M 50.14375 82.427751 \n",
       "L 245.44375 82.427751 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#m4956b7ea0d\" y=\"82.427751\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- 0.10 -->\n",
       "      <g transform=\"translate(20.878125 86.22697)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <path clip-path=\"url(#p35e391b3b5)\" d=\"M 50.14375 42.304281 \n",
       "L 245.44375 42.304281 \n",
       "\" style=\"fill:none;stroke:#b0b0b0;stroke-linecap:square;stroke-width:0.8;\"/>\n",
       "     </g>\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"50.14375\" xlink:href=\"#m4956b7ea0d\" y=\"42.304281\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0.15 -->\n",
       "      <g transform=\"translate(20.878125 46.1035)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"159.033203\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_9\">\n",
       "     <!-- loss -->\n",
       "     <g transform=\"translate(14.798437 84.807812)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-108\"/>\n",
       "       <path d=\"M 44.28125 53.078125 \n",
       "L 44.28125 44.578125 \n",
       "Q 40.484375 46.53125 36.375 47.5 \n",
       "Q 32.28125 48.484375 27.875 48.484375 \n",
       "Q 21.1875 48.484375 17.84375 46.4375 \n",
       "Q 14.5 44.390625 14.5 40.28125 \n",
       "Q 14.5 37.15625 16.890625 35.375 \n",
       "Q 19.28125 33.59375 26.515625 31.984375 \n",
       "L 29.59375 31.296875 \n",
       "Q 39.15625 29.25 43.1875 25.515625 \n",
       "Q 47.21875 21.78125 47.21875 15.09375 \n",
       "Q 47.21875 7.46875 41.1875 3.015625 \n",
       "Q 35.15625 -1.421875 24.609375 -1.421875 \n",
       "Q 20.21875 -1.421875 15.453125 -0.5625 \n",
       "Q 10.6875 0.296875 5.421875 2 \n",
       "L 5.421875 11.28125 \n",
       "Q 10.40625 8.6875 15.234375 7.390625 \n",
       "Q 20.0625 6.109375 24.8125 6.109375 \n",
       "Q 31.15625 6.109375 34.5625 8.28125 \n",
       "Q 37.984375 10.453125 37.984375 14.40625 \n",
       "Q 37.984375 18.0625 35.515625 20.015625 \n",
       "Q 33.0625 21.96875 24.703125 23.78125 \n",
       "L 21.578125 24.515625 \n",
       "Q 13.234375 26.265625 9.515625 29.90625 \n",
       "Q 5.8125 33.546875 5.8125 39.890625 \n",
       "Q 5.8125 47.609375 11.28125 51.796875 \n",
       "Q 16.75 56 26.8125 56 \n",
       "Q 31.78125 56 36.171875 55.265625 \n",
       "Q 40.578125 54.546875 44.28125 53.078125 \n",
       "z\n",
       "\" id=\"DejaVuSans-115\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-108\"/>\n",
       "      <use x=\"27.783203\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"88.964844\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"141.064453\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path clip-path=\"url(#p35e391b3b5)\" d=\"M 50.14375 13.377273 \n",
       "L 60.422697 55.447916 \n",
       "L 70.701645 80.708866 \n",
       "L 80.980592 93.616195 \n",
       "L 91.259539 105.306677 \n",
       "L 101.538487 115.334439 \n",
       "L 111.817434 117.994542 \n",
       "L 122.096382 123.439557 \n",
       "L 132.375329 125.363654 \n",
       "L 142.654276 127.208174 \n",
       "L 152.933224 128.601574 \n",
       "L 163.212171 129.114058 \n",
       "L 173.491118 131.174008 \n",
       "L 183.770066 132.291204 \n",
       "L 194.049013 134.081308 \n",
       "L 204.327961 135.103456 \n",
       "L 214.606908 135.068869 \n",
       "L 224.885855 135.050468 \n",
       "L 235.164803 136.922727 \n",
       "L 245.44375 136.578948 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 50.14375 143.1 \n",
       "L 50.14375 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 245.44375 143.1 \n",
       "L 245.44375 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 50.14375 143.1 \n",
       "L 245.44375 143.1 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 50.14375 7.2 \n",
       "L 245.44375 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p35e391b3b5\">\n",
       "   <rect height=\"135.9\" width=\"195.3\" x=\"50.14375\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_hiddens, num_layers, dropout, batch_size, num_steps = 32, 2, 0.1, 64, 10 #2层\n",
    "\n",
    "lr, num_epochs, device = 0.005, 200, d2l.try_gpu()\n",
    "\n",
    "ffn_num_input, ffn_num_hiddens, num_heads = 32, 64, 4 #4头\n",
    "\n",
    "key_size, query_size, value_size = 32, 32, 32 #kqv是32，bert是1024\n",
    "norm_shape = [32]\n",
    "\n",
    "train_iter, src_vocab, tgt_vocab = d2l.load_data_nmt(batch_size, num_steps)\n",
    "\n",
    "encoder = TransformerEncoder(\n",
    "    len(src_vocab), key_size, query_size, value_size, num_hiddens,\n",
    "    norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,\n",
    "    num_layers, dropout)\n",
    "decoder = TransformerDecoder(\n",
    "    len(tgt_vocab), key_size, query_size, value_size, num_hiddens,\n",
    "    norm_shape, ffn_num_input, ffn_num_hiddens, num_heads,\n",
    "    num_layers, dropout)\n",
    "net = d2l.EncoderDecoder(encoder, decoder)\n",
    "d2l.train_seq2seq(net, train_iter, lr, num_epochs, tgt_vocab, device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 56
   },
   "source": [
    "训练结束后，使用transformer模型[**将一些英语句子翻译成法语**]，并且计算它们的BLEU分数。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "origin_pos": 57,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "go . => va !,  bleu 1.000\n",
      "i lost . => j'ai perdu .,  bleu 1.000\n",
      "he's calm . => il est calme .,  bleu 1.000\n",
      "i'm home . => je suis chez moi .,  bleu 1.000\n"
     ]
    }
   ],
   "source": [
    "engs = ['go .', \"i lost .\", 'he\\'s calm .', 'i\\'m home .']\n",
    "fras = ['va !', 'j\\'ai perdu .', 'il est calme .', 'je suis chez moi .']\n",
    "for eng, fra in zip(engs, fras):\n",
    "    translation, dec_attention_weight_seq = d2l.predict_seq2seq(\n",
    "        net, eng, src_vocab, tgt_vocab, num_steps, device, True)\n",
    "    print(f'{eng} => {translation}, ',\n",
    "          f'bleu {d2l.bleu(translation, fra, k=2):.3f}')\n",
    "# 现在bleu分数好像不错，都是1了"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 59
   },
   "source": [
    "当进行最后一个英语到法语的句子翻译工作时，让我们[**可视化transformer的注意力权重**]。编码器自注意力权重的形状为（编码器层数，注意力头数，`num_steps`或查询的数目，`num_steps`或“键－值”对的数目）。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "origin_pos": 60,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 4, 10, 10])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enc_attention_weights = torch.cat(net.encoder.attention_weights, 0).reshape((num_layers, num_heads,\n",
    "    -1, num_steps))\n",
    "enc_attention_weights.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 61
   },
   "source": [
    "在编码器的自注意力中，查询和键都来自相同的输入序列。因为填充词元是不携带信息的，因此通过指定输入序列的有效长度可以避免查询与使用填充词元的位置计算注意力。接下来，将逐行呈现两层多头注意力的权重。每个注意力头都根据查询、键和值的不同的表示子空间来表示不同的注意力。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "origin_pos": 63,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"231.582992pt\" version=\"1.1\" viewBox=\"0 0 402.06155 231.582992\" width=\"402.06155pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2021-12-08T21:38:44.772527</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.3.3, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 231.582992 \n",
       "L 402.06155 231.582992 \n",
       "L 402.06155 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 34.240625 90.24856 \n",
       "L 102.17106 90.24856 \n",
       "L 102.17106 22.318125 \n",
       "L 34.240625 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p920d6fc047)\">\n",
       "    <image height=\"68\" id=\"imageb11c9c1ddc\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"34.240625\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAAwklEQVR4nO3asQ3CMBBA0YQWRmA/GCkDMgBN6tA/ySloAtF/rWXJ+rrKuvkx3bZpYFlfo6PTuhz9gF9TEBQEBUFBUBAUBAVBQVAQFAQFQUFQEBQEBUFBUBAUBAVBQVAQFAQFQUFQEBQEBUFBUBAUBAVBQVAQFAQFQUFQEBQEBcG8re/h4u7zeh9ePOtSbxOCgqAgKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgINj9U/3Gv//DNiEoCAqCgqAgKAg+2M0SL1UnqaIAAAAASUVORK5CYII=\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m8587e77260\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"37.637147\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"71.602364\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"mc73e724ff0\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#mc73e724ff0\" y=\"25.714647\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(20.878125 29.513865)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#mc73e724ff0\" y=\"59.679864\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(20.878125 63.479083)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_3\">\n",
       "     <!-- Query positions -->\n",
       "     <g transform=\"translate(14.798437 95.477874)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 39.40625 66.21875 \n",
       "Q 28.65625 66.21875 22.328125 58.203125 \n",
       "Q 16.015625 50.203125 16.015625 36.375 \n",
       "Q 16.015625 22.609375 22.328125 14.59375 \n",
       "Q 28.65625 6.59375 39.40625 6.59375 \n",
       "Q 50.140625 6.59375 56.421875 14.59375 \n",
       "Q 62.703125 22.609375 62.703125 36.375 \n",
       "Q 62.703125 50.203125 56.421875 58.203125 \n",
       "Q 50.140625 66.21875 39.40625 66.21875 \n",
       "z\n",
       "M 53.21875 1.3125 \n",
       "L 66.21875 -12.890625 \n",
       "L 54.296875 -12.890625 \n",
       "L 43.5 -1.21875 \n",
       "Q 41.890625 -1.3125 41.03125 -1.359375 \n",
       "Q 40.1875 -1.421875 39.40625 -1.421875 \n",
       "Q 24.03125 -1.421875 14.8125 8.859375 \n",
       "Q 5.609375 19.140625 5.609375 36.375 \n",
       "Q 5.609375 53.65625 14.8125 63.9375 \n",
       "Q 24.03125 74.21875 39.40625 74.21875 \n",
       "Q 54.734375 74.21875 63.90625 63.9375 \n",
       "Q 73.09375 53.65625 73.09375 36.375 \n",
       "Q 73.09375 23.6875 67.984375 14.640625 \n",
       "Q 62.890625 5.609375 53.21875 1.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-81\"/>\n",
       "       <path d=\"M 8.5 21.578125 \n",
       "L 8.5 54.6875 \n",
       "L 17.484375 54.6875 \n",
       "L 17.484375 21.921875 \n",
       "Q 17.484375 14.15625 20.5 10.265625 \n",
       "Q 23.53125 6.390625 29.59375 6.390625 \n",
       "Q 36.859375 6.390625 41.078125 11.03125 \n",
       "Q 45.3125 15.671875 45.3125 23.6875 \n",
       "L 45.3125 54.6875 \n",
       "L 54.296875 54.6875 \n",
       "L 54.296875 0 \n",
       "L 45.3125 0 \n",
       "L 45.3125 8.40625 \n",
       "Q 42.046875 3.421875 37.71875 1 \n",
       "Q 33.40625 -1.421875 27.6875 -1.421875 \n",
       "Q 18.265625 -1.421875 13.375 4.4375 \n",
       "Q 8.5 10.296875 8.5 21.578125 \n",
       "z\n",
       "M 31.109375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-117\"/>\n",
       "       <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "       <path d=\"M 41.109375 46.296875 \n",
       "Q 39.59375 47.171875 37.8125 47.578125 \n",
       "Q 36.03125 48 33.890625 48 \n",
       "Q 26.265625 48 22.1875 43.046875 \n",
       "Q 18.109375 38.09375 18.109375 28.8125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 20.953125 51.171875 25.484375 53.578125 \n",
       "Q 30.03125 56 36.53125 56 \n",
       "Q 37.453125 56 38.578125 55.875 \n",
       "Q 39.703125 55.765625 41.0625 55.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-114\"/>\n",
       "       <path d=\"M 32.171875 -5.078125 \n",
       "Q 28.375 -14.84375 24.75 -17.8125 \n",
       "Q 21.140625 -20.796875 15.09375 -20.796875 \n",
       "L 7.90625 -20.796875 \n",
       "L 7.90625 -13.28125 \n",
       "L 13.1875 -13.28125 \n",
       "Q 16.890625 -13.28125 18.9375 -11.515625 \n",
       "Q 21 -9.765625 23.484375 -3.21875 \n",
       "L 25.09375 0.875 \n",
       "L 2.984375 54.6875 \n",
       "L 12.5 54.6875 \n",
       "L 29.59375 11.921875 \n",
       "L 46.6875 54.6875 \n",
       "L 56.203125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-121\"/>\n",
       "       <path id=\"DejaVuSans-32\"/>\n",
       "       <path d=\"M 18.109375 8.203125 \n",
       "L 18.109375 -20.796875 \n",
       "L 9.078125 -20.796875 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.390625 \n",
       "Q 20.953125 51.265625 25.265625 53.625 \n",
       "Q 29.59375 56 35.59375 56 \n",
       "Q 45.5625 56 51.78125 48.09375 \n",
       "Q 58.015625 40.1875 58.015625 27.296875 \n",
       "Q 58.015625 14.40625 51.78125 6.484375 \n",
       "Q 45.5625 -1.421875 35.59375 -1.421875 \n",
       "Q 29.59375 -1.421875 25.265625 0.953125 \n",
       "Q 20.953125 3.328125 18.109375 8.203125 \n",
       "z\n",
       "M 48.6875 27.296875 \n",
       "Q 48.6875 37.203125 44.609375 42.84375 \n",
       "Q 40.53125 48.484375 33.40625 48.484375 \n",
       "Q 26.265625 48.484375 22.1875 42.84375 \n",
       "Q 18.109375 37.203125 18.109375 27.296875 \n",
       "Q 18.109375 17.390625 22.1875 11.75 \n",
       "Q 26.265625 6.109375 33.40625 6.109375 \n",
       "Q 40.53125 6.109375 44.609375 11.75 \n",
       "Q 48.6875 17.390625 48.6875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-112\"/>\n",
       "       <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "       <path d=\"M 44.28125 53.078125 \n",
       "L 44.28125 44.578125 \n",
       "Q 40.484375 46.53125 36.375 47.5 \n",
       "Q 32.28125 48.484375 27.875 48.484375 \n",
       "Q 21.1875 48.484375 17.84375 46.4375 \n",
       "Q 14.5 44.390625 14.5 40.28125 \n",
       "Q 14.5 37.15625 16.890625 35.375 \n",
       "Q 19.28125 33.59375 26.515625 31.984375 \n",
       "L 29.59375 31.296875 \n",
       "Q 39.15625 29.25 43.1875 25.515625 \n",
       "Q 47.21875 21.78125 47.21875 15.09375 \n",
       "Q 47.21875 7.46875 41.1875 3.015625 \n",
       "Q 35.15625 -1.421875 24.609375 -1.421875 \n",
       "Q 20.21875 -1.421875 15.453125 -0.5625 \n",
       "Q 10.6875 0.296875 5.421875 2 \n",
       "L 5.421875 11.28125 \n",
       "Q 10.40625 8.6875 15.234375 7.390625 \n",
       "Q 20.0625 6.109375 24.8125 6.109375 \n",
       "Q 31.15625 6.109375 34.5625 8.28125 \n",
       "Q 37.984375 10.453125 37.984375 14.40625 \n",
       "Q 37.984375 18.0625 35.515625 20.015625 \n",
       "Q 33.0625 21.96875 24.703125 23.78125 \n",
       "L 21.578125 24.515625 \n",
       "Q 13.234375 26.265625 9.515625 29.90625 \n",
       "Q 5.8125 33.546875 5.8125 39.890625 \n",
       "Q 5.8125 47.609375 11.28125 51.796875 \n",
       "Q 16.75 56 26.8125 56 \n",
       "Q 31.78125 56 36.171875 55.265625 \n",
       "Q 40.578125 54.546875 44.28125 53.078125 \n",
       "z\n",
       "\" id=\"DejaVuSans-115\"/>\n",
       "       <path d=\"M 9.421875 54.6875 \n",
       "L 18.40625 54.6875 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 64.59375 \n",
       "L 9.421875 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-105\"/>\n",
       "       <path d=\"M 18.3125 70.21875 \n",
       "L 18.3125 54.6875 \n",
       "L 36.8125 54.6875 \n",
       "L 36.8125 47.703125 \n",
       "L 18.3125 47.703125 \n",
       "L 18.3125 18.015625 \n",
       "Q 18.3125 11.328125 20.140625 9.421875 \n",
       "Q 21.96875 7.515625 27.59375 7.515625 \n",
       "L 36.8125 7.515625 \n",
       "L 36.8125 0 \n",
       "L 27.59375 0 \n",
       "Q 17.1875 0 13.234375 3.875 \n",
       "Q 9.28125 7.765625 9.28125 18.015625 \n",
       "L 9.28125 47.703125 \n",
       "L 2.6875 47.703125 \n",
       "L 2.6875 54.6875 \n",
       "L 9.28125 54.6875 \n",
       "L 9.28125 70.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-116\"/>\n",
       "       <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-110\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-81\"/>\n",
       "      <use x=\"78.710938\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"142.089844\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"203.613281\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"244.726562\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"303.90625\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"335.693359\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"399.169922\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"460.351562\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"512.451172\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"540.234375\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"579.443359\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"607.226562\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"668.408203\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"731.787109\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 34.240625 90.24856 \n",
       "L 34.240625 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 102.17106 90.24856 \n",
       "L 102.17106 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 34.240625 90.24856 \n",
       "L 102.17106 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 34.240625 22.318125 \n",
       "L 102.17106 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_4\">\n",
       "    <!-- Head 1 -->\n",
       "    <g transform=\"translate(46.791467 16.318125)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 9.8125 72.90625 \n",
       "L 19.671875 72.90625 \n",
       "L 19.671875 43.015625 \n",
       "L 55.515625 43.015625 \n",
       "L 55.515625 72.90625 \n",
       "L 65.375 72.90625 \n",
       "L 65.375 0 \n",
       "L 55.515625 0 \n",
       "L 55.515625 34.71875 \n",
       "L 19.671875 34.71875 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-72\"/>\n",
       "      <path d=\"M 34.28125 27.484375 \n",
       "Q 23.390625 27.484375 19.1875 25 \n",
       "Q 14.984375 22.515625 14.984375 16.5 \n",
       "Q 14.984375 11.71875 18.140625 8.90625 \n",
       "Q 21.296875 6.109375 26.703125 6.109375 \n",
       "Q 34.1875 6.109375 38.703125 11.40625 \n",
       "Q 43.21875 16.703125 43.21875 25.484375 \n",
       "L 43.21875 27.484375 \n",
       "z\n",
       "M 52.203125 31.203125 \n",
       "L 52.203125 0 \n",
       "L 43.21875 0 \n",
       "L 43.21875 8.296875 \n",
       "Q 40.140625 3.328125 35.546875 0.953125 \n",
       "Q 30.953125 -1.421875 24.3125 -1.421875 \n",
       "Q 15.921875 -1.421875 10.953125 3.296875 \n",
       "Q 6 8.015625 6 15.921875 \n",
       "Q 6 25.140625 12.171875 29.828125 \n",
       "Q 18.359375 34.515625 30.609375 34.515625 \n",
       "L 43.21875 34.515625 \n",
       "L 43.21875 35.40625 \n",
       "Q 43.21875 41.609375 39.140625 45 \n",
       "Q 35.0625 48.390625 27.6875 48.390625 \n",
       "Q 23 48.390625 18.546875 47.265625 \n",
       "Q 14.109375 46.140625 10.015625 43.890625 \n",
       "L 10.015625 52.203125 \n",
       "Q 14.9375 54.109375 19.578125 55.046875 \n",
       "Q 24.21875 56 28.609375 56 \n",
       "Q 40.484375 56 46.34375 49.84375 \n",
       "Q 52.203125 43.703125 52.203125 31.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-97\"/>\n",
       "      <path d=\"M 45.40625 46.390625 \n",
       "L 45.40625 75.984375 \n",
       "L 54.390625 75.984375 \n",
       "L 54.390625 0 \n",
       "L 45.40625 0 \n",
       "L 45.40625 8.203125 \n",
       "Q 42.578125 3.328125 38.25 0.953125 \n",
       "Q 33.9375 -1.421875 27.875 -1.421875 \n",
       "Q 17.96875 -1.421875 11.734375 6.484375 \n",
       "Q 5.515625 14.40625 5.515625 27.296875 \n",
       "Q 5.515625 40.1875 11.734375 48.09375 \n",
       "Q 17.96875 56 27.875 56 \n",
       "Q 33.9375 56 38.25 53.625 \n",
       "Q 42.578125 51.265625 45.40625 46.390625 \n",
       "z\n",
       "M 14.796875 27.296875 \n",
       "Q 14.796875 17.390625 18.875 11.75 \n",
       "Q 22.953125 6.109375 30.078125 6.109375 \n",
       "Q 37.203125 6.109375 41.296875 11.75 \n",
       "Q 45.40625 17.390625 45.40625 27.296875 \n",
       "Q 45.40625 37.203125 41.296875 42.84375 \n",
       "Q 37.203125 48.484375 30.078125 48.484375 \n",
       "Q 22.953125 48.484375 18.875 42.84375 \n",
       "Q 14.796875 37.203125 14.796875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-100\"/>\n",
       "      <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g id=\"patch_7\">\n",
       "    <path d=\"M 115.757147 90.24856 \n",
       "L 183.687582 90.24856 \n",
       "L 183.687582 22.318125 \n",
       "L 115.757147 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pb87c0e8598)\">\n",
       "    <image height=\"68\" id=\"imagef6683b6d01\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"115.757147\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAA1UlEQVR4nO3bsY0CMRRAQcxBBCVcf1ASBV4BJISwxDxB4oADaSa05LX19EPvWC7nZTXhuPt9un66/M187mOs//sCn0aQECQECUFCkBAkBAlBQpAQJAQJQUKQECQECUFCkBAkBAlBQpAQJAQJQUKQECQECUFCkBAkBAlBQpAQJAQJQUKQECQEiXFY7V8+3P32R7gzTEgIEoKEICFICBKChCAhSAgSgoQgMfyV+ciEhCAhSAgSgoQgsZnduB3j6fpyu77cM9Y/s8e9jQkJQUKQECQECUHiDihbFTi7xo9ZAAAAAElFTkSuQmCC\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_3\">\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"119.153668\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"153.118886\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_4\">\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#mc73e724ff0\" y=\"25.714647\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#mc73e724ff0\" y=\"59.679864\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"M 115.757147 90.24856 \n",
       "L 115.757147 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path d=\"M 183.687582 90.24856 \n",
       "L 183.687582 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path d=\"M 115.757147 90.24856 \n",
       "L 183.687582 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path d=\"M 115.757147 22.318125 \n",
       "L 183.687582 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_5\">\n",
       "    <!-- Head 2 -->\n",
       "    <g transform=\"translate(128.307989 16.318125)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_3\">\n",
       "   <g id=\"patch_12\">\n",
       "    <path d=\"M 197.273668 90.24856 \n",
       "L 265.204103 90.24856 \n",
       "L 265.204103 22.318125 \n",
       "L 197.273668 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pf33b00330f)\">\n",
       "    <image height=\"68\" id=\"image633b4b901e\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"197.273668\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAAyElEQVR4nO3bsQ3CMBRAwYQWRmA/GIkBGYAmdehPcoOMINK71oWtJzeWvtd9e+3LRPfzdbj22J4zt/qK068P8G8KgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgIFhvy2U4uHuEQdvZuiEoCAqCgqAgKAgKgoKgICgICoKCYP30V+bo9+XRH4TdEBQEBUFBUBAUBAVBQVAQFAQFQUFQELwBJVgSL3cgArkAAAAASUVORK5CYII=\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_5\">\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"200.67019\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"234.635408\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_6\">\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#mc73e724ff0\" y=\"25.714647\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#mc73e724ff0\" y=\"59.679864\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_13\">\n",
       "    <path d=\"M 197.273668 90.24856 \n",
       "L 197.273668 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_14\">\n",
       "    <path d=\"M 265.204103 90.24856 \n",
       "L 265.204103 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_15\">\n",
       "    <path d=\"M 197.273668 90.24856 \n",
       "L 265.204103 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_16\">\n",
       "    <path d=\"M 197.273668 22.318125 \n",
       "L 265.204103 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_6\">\n",
       "    <!-- Head 3 -->\n",
       "    <g transform=\"translate(209.824511 16.318125)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_4\">\n",
       "   <g id=\"patch_17\">\n",
       "    <path d=\"M 278.79019 90.24856 \n",
       "L 346.720625 90.24856 \n",
       "L 346.720625 22.318125 \n",
       "L 278.79019 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pe9f6adbc36)\">\n",
       "    <image height=\"68\" id=\"image82eaf80ee9\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"278.79019\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAAxklEQVR4nO3bsQ0CMRAAQT8plEB/UBIFUgDJx08+wgQk8GgntBNrZemiWy7jtI2J23qfXf2tw7cf8GsKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgIlm19TLcy37kezy/P977J2Q9BQVAQFAQFQUHw8didmY3jMfYxkvshKAgKgoKgICgInh3mEi+yYkxoAAAAAElFTkSuQmCC\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_7\">\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.186712\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"316.151929\" xlink:href=\"#m8587e77260\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_8\">\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#mc73e724ff0\" y=\"25.714647\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#mc73e724ff0\" y=\"59.679864\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_18\">\n",
       "    <path d=\"M 278.79019 90.24856 \n",
       "L 278.79019 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_19\">\n",
       "    <path d=\"M 346.720625 90.24856 \n",
       "L 346.720625 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_20\">\n",
       "    <path d=\"M 278.79019 90.24856 \n",
       "L 346.720625 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_21\">\n",
       "    <path d=\"M 278.79019 22.318125 \n",
       "L 346.720625 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_7\">\n",
       "    <!-- Head 4 -->\n",
       "    <g transform=\"translate(291.341033 16.318125)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_5\">\n",
       "   <g id=\"patch_22\">\n",
       "    <path d=\"M 34.240625 194.026742 \n",
       "L 102.17106 194.026742 \n",
       "L 102.17106 126.096307 \n",
       "L 34.240625 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pf45512603d)\">\n",
       "    <image height=\"68\" id=\"image2d822173d4\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"34.240625\" xlink:href=\"data:image/png;base64,\n",
       "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\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_9\">\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"37.637147\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(34.455897 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"71.602364\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(68.421114 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_10\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(35.142561 222.303304)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 9.8125 72.90625 \n",
       "L 19.671875 72.90625 \n",
       "L 19.671875 42.09375 \n",
       "L 52.390625 72.90625 \n",
       "L 65.09375 72.90625 \n",
       "L 28.90625 38.921875 \n",
       "L 67.671875 0 \n",
       "L 54.6875 0 \n",
       "L 19.671875 35.109375 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-75\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_10\">\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#mc73e724ff0\" y=\"129.492829\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(20.878125 133.292047)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_10\">\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#mc73e724ff0\" y=\"163.458046\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(20.878125 167.257265)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- Query positions -->\n",
       "     <g transform=\"translate(14.798437 199.256055)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-81\"/>\n",
       "      <use x=\"78.710938\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"142.089844\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"203.613281\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"244.726562\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"303.90625\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"335.693359\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"399.169922\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"460.351562\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"512.451172\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"540.234375\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"579.443359\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"607.226562\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"668.408203\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"731.787109\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_23\">\n",
       "    <path d=\"M 34.240625 194.026742 \n",
       "L 34.240625 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_24\">\n",
       "    <path d=\"M 102.17106 194.026742 \n",
       "L 102.17106 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_25\">\n",
       "    <path d=\"M 34.240625 194.026742 \n",
       "L 102.17106 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_26\">\n",
       "    <path d=\"M 34.240625 126.096307 \n",
       "L 102.17106 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_14\">\n",
       "    <!-- Head 1 -->\n",
       "    <g transform=\"translate(46.791467 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_6\">\n",
       "   <g id=\"patch_27\">\n",
       "    <path d=\"M 115.757147 194.026742 \n",
       "L 183.687582 194.026742 \n",
       "L 183.687582 126.096307 \n",
       "L 115.757147 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pa43a31e519)\">\n",
       "    <image height=\"68\" id=\"imagee09d8c9837\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"115.757147\" xlink:href=\"data:image/png;base64,\n",
       "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\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_11\">\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"119.153668\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(115.972418 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"153.118886\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(149.937636 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_17\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(116.659083 222.303304)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_12\">\n",
       "    <g id=\"ytick_11\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#mc73e724ff0\" y=\"129.492829\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_12\">\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#mc73e724ff0\" y=\"163.458046\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_28\">\n",
       "    <path d=\"M 115.757147 194.026742 \n",
       "L 115.757147 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_29\">\n",
       "    <path d=\"M 183.687582 194.026742 \n",
       "L 183.687582 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_30\">\n",
       "    <path d=\"M 115.757147 194.026742 \n",
       "L 183.687582 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_31\">\n",
       "    <path d=\"M 115.757147 126.096307 \n",
       "L 183.687582 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_18\">\n",
       "    <!-- Head 2 -->\n",
       "    <g transform=\"translate(128.307989 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_7\">\n",
       "   <g id=\"patch_32\">\n",
       "    <path d=\"M 197.273668 194.026742 \n",
       "L 265.204103 194.026742 \n",
       "L 265.204103 126.096307 \n",
       "L 197.273668 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pafe5e7d866)\">\n",
       "    <image height=\"68\" id=\"image17b06c0a5c\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"197.273668\" xlink:href=\"data:image/png;base64,\n",
       "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\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_13\">\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"200.67019\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(197.48894 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"234.635408\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(231.454158 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_21\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(198.175605 222.303304)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_14\">\n",
       "    <g id=\"ytick_13\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#mc73e724ff0\" y=\"129.492829\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_14\">\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#mc73e724ff0\" y=\"163.458046\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_33\">\n",
       "    <path d=\"M 197.273668 194.026742 \n",
       "L 197.273668 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_34\">\n",
       "    <path d=\"M 265.204103 194.026742 \n",
       "L 265.204103 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_35\">\n",
       "    <path d=\"M 197.273668 194.026742 \n",
       "L 265.204103 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_36\">\n",
       "    <path d=\"M 197.273668 126.096307 \n",
       "L 265.204103 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_22\">\n",
       "    <!-- Head 3 -->\n",
       "    <g transform=\"translate(209.824511 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_8\">\n",
       "   <g id=\"patch_37\">\n",
       "    <path d=\"M 278.79019 194.026742 \n",
       "L 346.720625 194.026742 \n",
       "L 346.720625 126.096307 \n",
       "L 278.79019 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pfdb751ef64)\">\n",
       "    <image height=\"68\" id=\"imagee29c80b467\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"278.79019\" xlink:href=\"data:image/png;base64,\n",
       "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\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_15\">\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.186712\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(279.005462 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"316.151929\" xlink:href=\"#m8587e77260\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(312.970679 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_25\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(279.692126 222.303304)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_16\">\n",
       "    <g id=\"ytick_15\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#mc73e724ff0\" y=\"129.492829\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_16\">\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#mc73e724ff0\" y=\"163.458046\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_38\">\n",
       "    <path d=\"M 278.79019 194.026742 \n",
       "L 278.79019 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_39\">\n",
       "    <path d=\"M 346.720625 194.026742 \n",
       "L 346.720625 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_40\">\n",
       "    <path d=\"M 278.79019 194.026742 \n",
       "L 346.720625 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_41\">\n",
       "    <path d=\"M 278.79019 126.096307 \n",
       "L 346.720625 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_26\">\n",
       "    <!-- Head 4 -->\n",
       "    <g transform=\"translate(291.341033 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_9\">\n",
       "   <g id=\"patch_42\">\n",
       "    <path clip-path=\"url(#p0085a8129f)\" d=\"M 366.250625 165.250433 \n",
       "L 366.250625 164.804511 \n",
       "L 366.250625 51.540355 \n",
       "L 366.250625 51.094433 \n",
       "L 371.958425 51.094433 \n",
       "L 371.958425 51.540355 \n",
       "L 371.958425 164.804511 \n",
       "L 371.958425 165.250433 \n",
       "z\n",
       "\" style=\"fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;\"/>\n",
       "   </g>\n",
       "   <image height=\"114\" id=\"image8924db3ec0\" transform=\"scale(1 -1)translate(0 -114)\" width=\"6\" x=\"366\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAAYAAAByCAYAAABwf6CfAAAAyElEQVR4nL2VSQ7EMAgEieT/fzWXnMYs8wHKUkcoOYK6CzCOr3rusuZbVtnFT4kMSrSIN4xihlwu9/GBwjdZYYOQqCBFyAy0QoU7KSBxOEGdMdgHzUq34vOgZcCDYqu5IU42OJfAG8XLQL+MQYZuJXdevCXYICU2MXhWKjz3XLl6wtWrlgFPUdIbFWQVpDgw2rgtx3KRIcNd7vwFAxVF023DJ4X3cVtpCAdFkCKwXBmOCmTAkhwUOBInxZ6zQsXvA8amhdOtSPEH+zQMSlnMFgMAAAAASUVORK5CYII=\" y=\"-51\"/>\n",
       "   <g id=\"matplotlib.axis_17\"/>\n",
       "   <g id=\"matplotlib.axis_18\">\n",
       "    <g id=\"ytick_17\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 3.5 0 \n",
       "\" id=\"md82cbc78c6\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#md82cbc78c6\" y=\"165.250433\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_27\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(378.958425 169.049652)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_18\">\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#md82cbc78c6\" y=\"141.4105\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_28\">\n",
       "      <!-- 0.2 -->\n",
       "      <g transform=\"translate(378.958425 145.209719)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_19\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#md82cbc78c6\" y=\"117.570567\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_29\">\n",
       "      <!-- 0.4 -->\n",
       "      <g transform=\"translate(378.958425 121.369786)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_20\">\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#md82cbc78c6\" y=\"93.730635\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_30\">\n",
       "      <!-- 0.6 -->\n",
       "      <g transform=\"translate(378.958425 97.529853)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 33.015625 40.375 \n",
       "Q 26.375 40.375 22.484375 35.828125 \n",
       "Q 18.609375 31.296875 18.609375 23.390625 \n",
       "Q 18.609375 15.53125 22.484375 10.953125 \n",
       "Q 26.375 6.390625 33.015625 6.390625 \n",
       "Q 39.65625 6.390625 43.53125 10.953125 \n",
       "Q 47.40625 15.53125 47.40625 23.390625 \n",
       "Q 47.40625 31.296875 43.53125 35.828125 \n",
       "Q 39.65625 40.375 33.015625 40.375 \n",
       "z\n",
       "M 52.59375 71.296875 \n",
       "L 52.59375 62.3125 \n",
       "Q 48.875 64.0625 45.09375 64.984375 \n",
       "Q 41.3125 65.921875 37.59375 65.921875 \n",
       "Q 27.828125 65.921875 22.671875 59.328125 \n",
       "Q 17.53125 52.734375 16.796875 39.40625 \n",
       "Q 19.671875 43.65625 24.015625 45.921875 \n",
       "Q 28.375 48.1875 33.59375 48.1875 \n",
       "Q 44.578125 48.1875 50.953125 41.515625 \n",
       "Q 57.328125 34.859375 57.328125 23.390625 \n",
       "Q 57.328125 12.15625 50.6875 5.359375 \n",
       "Q 44.046875 -1.421875 33.015625 -1.421875 \n",
       "Q 20.359375 -1.421875 13.671875 8.265625 \n",
       "Q 6.984375 17.96875 6.984375 36.375 \n",
       "Q 6.984375 53.65625 15.1875 63.9375 \n",
       "Q 23.390625 74.21875 37.203125 74.21875 \n",
       "Q 40.921875 74.21875 44.703125 73.484375 \n",
       "Q 48.484375 72.75 52.59375 71.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-54\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-54\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_21\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#md82cbc78c6\" y=\"69.890702\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_31\">\n",
       "      <!-- 0.8 -->\n",
       "      <g transform=\"translate(378.958425 73.68992)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 31.78125 34.625 \n",
       "Q 24.75 34.625 20.71875 30.859375 \n",
       "Q 16.703125 27.09375 16.703125 20.515625 \n",
       "Q 16.703125 13.921875 20.71875 10.15625 \n",
       "Q 24.75 6.390625 31.78125 6.390625 \n",
       "Q 38.8125 6.390625 42.859375 10.171875 \n",
       "Q 46.921875 13.96875 46.921875 20.515625 \n",
       "Q 46.921875 27.09375 42.890625 30.859375 \n",
       "Q 38.875 34.625 31.78125 34.625 \n",
       "z\n",
       "M 21.921875 38.8125 \n",
       "Q 15.578125 40.375 12.03125 44.71875 \n",
       "Q 8.5 49.078125 8.5 55.328125 \n",
       "Q 8.5 64.0625 14.71875 69.140625 \n",
       "Q 20.953125 74.21875 31.78125 74.21875 \n",
       "Q 42.671875 74.21875 48.875 69.140625 \n",
       "Q 55.078125 64.0625 55.078125 55.328125 \n",
       "Q 55.078125 49.078125 51.53125 44.71875 \n",
       "Q 48 40.375 41.703125 38.8125 \n",
       "Q 48.828125 37.15625 52.796875 32.3125 \n",
       "Q 56.78125 27.484375 56.78125 20.515625 \n",
       "Q 56.78125 9.90625 50.3125 4.234375 \n",
       "Q 43.84375 -1.421875 31.78125 -1.421875 \n",
       "Q 19.734375 -1.421875 13.25 4.234375 \n",
       "Q 6.78125 9.90625 6.78125 20.515625 \n",
       "Q 6.78125 27.484375 10.78125 32.3125 \n",
       "Q 14.796875 37.15625 21.921875 38.8125 \n",
       "z\n",
       "M 18.3125 54.390625 \n",
       "Q 18.3125 48.734375 21.84375 45.5625 \n",
       "Q 25.390625 42.390625 31.78125 42.390625 \n",
       "Q 38.140625 42.390625 41.71875 45.5625 \n",
       "Q 45.3125 48.734375 45.3125 54.390625 \n",
       "Q 45.3125 60.0625 41.71875 63.234375 \n",
       "Q 38.140625 66.40625 31.78125 66.40625 \n",
       "Q 25.390625 66.40625 21.84375 63.234375 \n",
       "Q 18.3125 60.0625 18.3125 54.390625 \n",
       "z\n",
       "\" id=\"DejaVuSans-56\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-56\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_43\">\n",
       "    <path d=\"M 366.250625 165.250433 \n",
       "L 366.250625 164.804511 \n",
       "L 366.250625 51.540355 \n",
       "L 366.250625 51.094433 \n",
       "L 371.958425 51.094433 \n",
       "L 371.958425 51.540355 \n",
       "L 371.958425 164.804511 \n",
       "L 371.958425 165.250433 \n",
       "z\n",
       "\" style=\"fill:none;stroke:#000000;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p920d6fc047\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"34.240625\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pb87c0e8598\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"115.757147\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pf33b00330f\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"197.273668\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pe9f6adbc36\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"278.79019\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pf45512603d\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"34.240625\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pa43a31e519\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"115.757147\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pafe5e7d866\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"197.273668\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pfdb751ef64\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"278.79019\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p0085a8129f\">\n",
       "   <rect height=\"114.156\" width=\"5.7078\" x=\"366.250625\" y=\"51.094433\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 504x252 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d2l.show_heatmaps(\n",
    "    enc_attention_weights.cpu(), xlabel='Key positions',\n",
    "    ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],\n",
    "    figsize=(7, 3.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 64
   },
   "source": [
    "[**为了可视化解码器的自注意力权重和“编码器－解码器”的注意力权重，我们需要完成更多的数据操作工作。**]例如，我们用零填充被掩蔽住的注意力权重。值得注意的是，解码器的自注意力权重和“编码器－解码器”的注意力权重都有相同的查询：即以*序列开始词元*（beginning-of-sequence,BOS）打头，再与后续输出的词元共同组成序列。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "origin_pos": 66,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([2, 4, 6, 10]), torch.Size([2, 4, 6, 10]))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dec_attention_weights_2d = [head[0].tolist()\n",
    "                            for step in dec_attention_weight_seq\n",
    "                            for attn in step for blk in attn for head in blk]\n",
    "dec_attention_weights_filled = torch.tensor(\n",
    "    pd.DataFrame(dec_attention_weights_2d).fillna(0.0).values)\n",
    "dec_attention_weights = dec_attention_weights_filled.reshape((-1, 2, num_layers, num_heads, num_steps))\n",
    "dec_self_attention_weights, dec_inter_attention_weights = \\\n",
    "    dec_attention_weights.permute(1, 2, 3, 0, 4)\n",
    "dec_self_attention_weights.shape, dec_inter_attention_weights.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 68
   },
   "source": [
    "由于解码器自注意力的自回归属性，查询不会对当前位置之后的“键－值”对进行注意力计算。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "origin_pos": 69,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"231.582992pt\" version=\"1.1\" viewBox=\"0 0 402.06155 231.582992\" width=\"402.06155pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2021-12-08T21:38:45.555224</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.3.3, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 231.582992 \n",
       "L 402.06155 231.582992 \n",
       "L 402.06155 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 34.240625 90.24856 \n",
       "L 102.17106 90.24856 \n",
       "L 102.17106 22.318125 \n",
       "L 34.240625 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pa7f80fb90b)\">\n",
       "    <image height=\"68\" id=\"image94cd5522a4\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"34.240625\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAA1UlEQVR4nO3aOw6CUBBAUTB2ugT3p0tygS7Ahhr7W/EKEjDn1IS83EwxfOZ1+a7Tn3vdHpuvvex4jlMSJAQJQUKQECQECUFCkBAk5qOs7iPr9Xv57HYOExKChCAhSAgSgoQgIUgIEoKEIHHd8+ZHeT4ZYUJCkBAkBAlBQpAQJAQJQUKQmJ/TffNniKOs13syISFICBKChCAhSAgSgoQgIUgM/UE08hZ9ms656puQECQECUFCkBAkBAlBQpAQJAQJnyHChIQgIUgIEoKEICFICBKChCDxA/YkHYSRgO6TAAAAAElFTkSuQmCC\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m5b4ee4c6f1\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"39.901495\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"96.51019\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m4e54e57180\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m4e54e57180\" y=\"27.978995\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(20.878125 31.778213)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m4e54e57180\" y=\"50.622473\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(20.878125 54.421692)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m4e54e57180\" y=\"73.265951\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 4 -->\n",
       "      <g transform=\"translate(20.878125 77.06517)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_4\">\n",
       "     <!-- Query positions -->\n",
       "     <g transform=\"translate(14.798437 95.477874)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 39.40625 66.21875 \n",
       "Q 28.65625 66.21875 22.328125 58.203125 \n",
       "Q 16.015625 50.203125 16.015625 36.375 \n",
       "Q 16.015625 22.609375 22.328125 14.59375 \n",
       "Q 28.65625 6.59375 39.40625 6.59375 \n",
       "Q 50.140625 6.59375 56.421875 14.59375 \n",
       "Q 62.703125 22.609375 62.703125 36.375 \n",
       "Q 62.703125 50.203125 56.421875 58.203125 \n",
       "Q 50.140625 66.21875 39.40625 66.21875 \n",
       "z\n",
       "M 53.21875 1.3125 \n",
       "L 66.21875 -12.890625 \n",
       "L 54.296875 -12.890625 \n",
       "L 43.5 -1.21875 \n",
       "Q 41.890625 -1.3125 41.03125 -1.359375 \n",
       "Q 40.1875 -1.421875 39.40625 -1.421875 \n",
       "Q 24.03125 -1.421875 14.8125 8.859375 \n",
       "Q 5.609375 19.140625 5.609375 36.375 \n",
       "Q 5.609375 53.65625 14.8125 63.9375 \n",
       "Q 24.03125 74.21875 39.40625 74.21875 \n",
       "Q 54.734375 74.21875 63.90625 63.9375 \n",
       "Q 73.09375 53.65625 73.09375 36.375 \n",
       "Q 73.09375 23.6875 67.984375 14.640625 \n",
       "Q 62.890625 5.609375 53.21875 1.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-81\"/>\n",
       "       <path d=\"M 8.5 21.578125 \n",
       "L 8.5 54.6875 \n",
       "L 17.484375 54.6875 \n",
       "L 17.484375 21.921875 \n",
       "Q 17.484375 14.15625 20.5 10.265625 \n",
       "Q 23.53125 6.390625 29.59375 6.390625 \n",
       "Q 36.859375 6.390625 41.078125 11.03125 \n",
       "Q 45.3125 15.671875 45.3125 23.6875 \n",
       "L 45.3125 54.6875 \n",
       "L 54.296875 54.6875 \n",
       "L 54.296875 0 \n",
       "L 45.3125 0 \n",
       "L 45.3125 8.40625 \n",
       "Q 42.046875 3.421875 37.71875 1 \n",
       "Q 33.40625 -1.421875 27.6875 -1.421875 \n",
       "Q 18.265625 -1.421875 13.375 4.4375 \n",
       "Q 8.5 10.296875 8.5 21.578125 \n",
       "z\n",
       "M 31.109375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-117\"/>\n",
       "       <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "       <path d=\"M 41.109375 46.296875 \n",
       "Q 39.59375 47.171875 37.8125 47.578125 \n",
       "Q 36.03125 48 33.890625 48 \n",
       "Q 26.265625 48 22.1875 43.046875 \n",
       "Q 18.109375 38.09375 18.109375 28.8125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 20.953125 51.171875 25.484375 53.578125 \n",
       "Q 30.03125 56 36.53125 56 \n",
       "Q 37.453125 56 38.578125 55.875 \n",
       "Q 39.703125 55.765625 41.0625 55.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-114\"/>\n",
       "       <path d=\"M 32.171875 -5.078125 \n",
       "Q 28.375 -14.84375 24.75 -17.8125 \n",
       "Q 21.140625 -20.796875 15.09375 -20.796875 \n",
       "L 7.90625 -20.796875 \n",
       "L 7.90625 -13.28125 \n",
       "L 13.1875 -13.28125 \n",
       "Q 16.890625 -13.28125 18.9375 -11.515625 \n",
       "Q 21 -9.765625 23.484375 -3.21875 \n",
       "L 25.09375 0.875 \n",
       "L 2.984375 54.6875 \n",
       "L 12.5 54.6875 \n",
       "L 29.59375 11.921875 \n",
       "L 46.6875 54.6875 \n",
       "L 56.203125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-121\"/>\n",
       "       <path id=\"DejaVuSans-32\"/>\n",
       "       <path d=\"M 18.109375 8.203125 \n",
       "L 18.109375 -20.796875 \n",
       "L 9.078125 -20.796875 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.390625 \n",
       "Q 20.953125 51.265625 25.265625 53.625 \n",
       "Q 29.59375 56 35.59375 56 \n",
       "Q 45.5625 56 51.78125 48.09375 \n",
       "Q 58.015625 40.1875 58.015625 27.296875 \n",
       "Q 58.015625 14.40625 51.78125 6.484375 \n",
       "Q 45.5625 -1.421875 35.59375 -1.421875 \n",
       "Q 29.59375 -1.421875 25.265625 0.953125 \n",
       "Q 20.953125 3.328125 18.109375 8.203125 \n",
       "z\n",
       "M 48.6875 27.296875 \n",
       "Q 48.6875 37.203125 44.609375 42.84375 \n",
       "Q 40.53125 48.484375 33.40625 48.484375 \n",
       "Q 26.265625 48.484375 22.1875 42.84375 \n",
       "Q 18.109375 37.203125 18.109375 27.296875 \n",
       "Q 18.109375 17.390625 22.1875 11.75 \n",
       "Q 26.265625 6.109375 33.40625 6.109375 \n",
       "Q 40.53125 6.109375 44.609375 11.75 \n",
       "Q 48.6875 17.390625 48.6875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-112\"/>\n",
       "       <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "       <path d=\"M 44.28125 53.078125 \n",
       "L 44.28125 44.578125 \n",
       "Q 40.484375 46.53125 36.375 47.5 \n",
       "Q 32.28125 48.484375 27.875 48.484375 \n",
       "Q 21.1875 48.484375 17.84375 46.4375 \n",
       "Q 14.5 44.390625 14.5 40.28125 \n",
       "Q 14.5 37.15625 16.890625 35.375 \n",
       "Q 19.28125 33.59375 26.515625 31.984375 \n",
       "L 29.59375 31.296875 \n",
       "Q 39.15625 29.25 43.1875 25.515625 \n",
       "Q 47.21875 21.78125 47.21875 15.09375 \n",
       "Q 47.21875 7.46875 41.1875 3.015625 \n",
       "Q 35.15625 -1.421875 24.609375 -1.421875 \n",
       "Q 20.21875 -1.421875 15.453125 -0.5625 \n",
       "Q 10.6875 0.296875 5.421875 2 \n",
       "L 5.421875 11.28125 \n",
       "Q 10.40625 8.6875 15.234375 7.390625 \n",
       "Q 20.0625 6.109375 24.8125 6.109375 \n",
       "Q 31.15625 6.109375 34.5625 8.28125 \n",
       "Q 37.984375 10.453125 37.984375 14.40625 \n",
       "Q 37.984375 18.0625 35.515625 20.015625 \n",
       "Q 33.0625 21.96875 24.703125 23.78125 \n",
       "L 21.578125 24.515625 \n",
       "Q 13.234375 26.265625 9.515625 29.90625 \n",
       "Q 5.8125 33.546875 5.8125 39.890625 \n",
       "Q 5.8125 47.609375 11.28125 51.796875 \n",
       "Q 16.75 56 26.8125 56 \n",
       "Q 31.78125 56 36.171875 55.265625 \n",
       "Q 40.578125 54.546875 44.28125 53.078125 \n",
       "z\n",
       "\" id=\"DejaVuSans-115\"/>\n",
       "       <path d=\"M 9.421875 54.6875 \n",
       "L 18.40625 54.6875 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 64.59375 \n",
       "L 9.421875 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-105\"/>\n",
       "       <path d=\"M 18.3125 70.21875 \n",
       "L 18.3125 54.6875 \n",
       "L 36.8125 54.6875 \n",
       "L 36.8125 47.703125 \n",
       "L 18.3125 47.703125 \n",
       "L 18.3125 18.015625 \n",
       "Q 18.3125 11.328125 20.140625 9.421875 \n",
       "Q 21.96875 7.515625 27.59375 7.515625 \n",
       "L 36.8125 7.515625 \n",
       "L 36.8125 0 \n",
       "L 27.59375 0 \n",
       "Q 17.1875 0 13.234375 3.875 \n",
       "Q 9.28125 7.765625 9.28125 18.015625 \n",
       "L 9.28125 47.703125 \n",
       "L 2.6875 47.703125 \n",
       "L 2.6875 54.6875 \n",
       "L 9.28125 54.6875 \n",
       "L 9.28125 70.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-116\"/>\n",
       "       <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-110\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-81\"/>\n",
       "      <use x=\"78.710938\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"142.089844\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"203.613281\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"244.726562\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"303.90625\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"335.693359\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"399.169922\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"460.351562\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"512.451172\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"540.234375\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"579.443359\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"607.226562\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"668.408203\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"731.787109\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 34.240625 90.24856 \n",
       "L 34.240625 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 102.17106 90.24856 \n",
       "L 102.17106 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 34.240625 90.24856 \n",
       "L 102.17106 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 34.240625 22.318125 \n",
       "L 102.17106 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_5\">\n",
       "    <!-- Head 1 -->\n",
       "    <g transform=\"translate(46.791467 16.318125)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 9.8125 72.90625 \n",
       "L 19.671875 72.90625 \n",
       "L 19.671875 43.015625 \n",
       "L 55.515625 43.015625 \n",
       "L 55.515625 72.90625 \n",
       "L 65.375 72.90625 \n",
       "L 65.375 0 \n",
       "L 55.515625 0 \n",
       "L 55.515625 34.71875 \n",
       "L 19.671875 34.71875 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-72\"/>\n",
       "      <path d=\"M 34.28125 27.484375 \n",
       "Q 23.390625 27.484375 19.1875 25 \n",
       "Q 14.984375 22.515625 14.984375 16.5 \n",
       "Q 14.984375 11.71875 18.140625 8.90625 \n",
       "Q 21.296875 6.109375 26.703125 6.109375 \n",
       "Q 34.1875 6.109375 38.703125 11.40625 \n",
       "Q 43.21875 16.703125 43.21875 25.484375 \n",
       "L 43.21875 27.484375 \n",
       "z\n",
       "M 52.203125 31.203125 \n",
       "L 52.203125 0 \n",
       "L 43.21875 0 \n",
       "L 43.21875 8.296875 \n",
       "Q 40.140625 3.328125 35.546875 0.953125 \n",
       "Q 30.953125 -1.421875 24.3125 -1.421875 \n",
       "Q 15.921875 -1.421875 10.953125 3.296875 \n",
       "Q 6 8.015625 6 15.921875 \n",
       "Q 6 25.140625 12.171875 29.828125 \n",
       "Q 18.359375 34.515625 30.609375 34.515625 \n",
       "L 43.21875 34.515625 \n",
       "L 43.21875 35.40625 \n",
       "Q 43.21875 41.609375 39.140625 45 \n",
       "Q 35.0625 48.390625 27.6875 48.390625 \n",
       "Q 23 48.390625 18.546875 47.265625 \n",
       "Q 14.109375 46.140625 10.015625 43.890625 \n",
       "L 10.015625 52.203125 \n",
       "Q 14.9375 54.109375 19.578125 55.046875 \n",
       "Q 24.21875 56 28.609375 56 \n",
       "Q 40.484375 56 46.34375 49.84375 \n",
       "Q 52.203125 43.703125 52.203125 31.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-97\"/>\n",
       "      <path d=\"M 45.40625 46.390625 \n",
       "L 45.40625 75.984375 \n",
       "L 54.390625 75.984375 \n",
       "L 54.390625 0 \n",
       "L 45.40625 0 \n",
       "L 45.40625 8.203125 \n",
       "Q 42.578125 3.328125 38.25 0.953125 \n",
       "Q 33.9375 -1.421875 27.875 -1.421875 \n",
       "Q 17.96875 -1.421875 11.734375 6.484375 \n",
       "Q 5.515625 14.40625 5.515625 27.296875 \n",
       "Q 5.515625 40.1875 11.734375 48.09375 \n",
       "Q 17.96875 56 27.875 56 \n",
       "Q 33.9375 56 38.25 53.625 \n",
       "Q 42.578125 51.265625 45.40625 46.390625 \n",
       "z\n",
       "M 14.796875 27.296875 \n",
       "Q 14.796875 17.390625 18.875 11.75 \n",
       "Q 22.953125 6.109375 30.078125 6.109375 \n",
       "Q 37.203125 6.109375 41.296875 11.75 \n",
       "Q 45.40625 17.390625 45.40625 27.296875 \n",
       "Q 45.40625 37.203125 41.296875 42.84375 \n",
       "Q 37.203125 48.484375 30.078125 48.484375 \n",
       "Q 22.953125 48.484375 18.875 42.84375 \n",
       "Q 14.796875 37.203125 14.796875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-100\"/>\n",
       "      <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g id=\"patch_7\">\n",
       "    <path d=\"M 115.757147 90.24856 \n",
       "L 183.687582 90.24856 \n",
       "L 183.687582 22.318125 \n",
       "L 115.757147 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p63d43f1299)\">\n",
       "    <image height=\"68\" id=\"image9935eece3d\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"115.757147\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAAzklEQVR4nO3ZsQ3CQBAAwTcplEB/UBIFUgCJY5NP5A8sZLQTO3itLriTl239bOPPPa/33d9eDnzHKRUEBUFBUBAUBAVBQVAQFATLzOo+swKPMcZrfU8/6NeaEBQEBUFBUBAUBAVBQVAQFAQFwdQtc6SZO+nIG6kJQUFQEBQEBUFBUBAUBAVBQbA8xm336n7G3wqzmhAUBAVBQVAQFAQFQUFQEBQEBUFBUBAUBAVBQVAQFAQFQUFQEBQEBUFBUBAUBAVBQVAQFAQFQUFQEHwBhkcWoCWpL4EAAAAASUVORK5CYII=\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_3\">\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"121.418016\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"178.026712\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_4\">\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m4e54e57180\" y=\"27.978995\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m4e54e57180\" y=\"50.622473\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m4e54e57180\" y=\"73.265951\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"M 115.757147 90.24856 \n",
       "L 115.757147 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path d=\"M 183.687582 90.24856 \n",
       "L 183.687582 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path d=\"M 115.757147 90.24856 \n",
       "L 183.687582 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path d=\"M 115.757147 22.318125 \n",
       "L 183.687582 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_6\">\n",
       "    <!-- Head 2 -->\n",
       "    <g transform=\"translate(128.307989 16.318125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_3\">\n",
       "   <g id=\"patch_12\">\n",
       "    <path d=\"M 197.273668 90.24856 \n",
       "L 265.204103 90.24856 \n",
       "L 265.204103 22.318125 \n",
       "L 197.273668 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p2f378f7a7d)\">\n",
       "    <image height=\"68\" id=\"image87f4bc27d1\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"197.273668\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAAzklEQVR4nO3aMQ6CQBBA0cXY6RG8nx7JA3oAG2rtf8UWJJC8V5MN+ZmC2bD81u9vHMDr9tj87Hv97PYel91OPilBQpAQJAQJQUKQECQECUHiuufhR/kcn2FCQpAQJAQJQUKQECQECUFCkBAkpnaZmd1kjOPsJzNMSAgSgoQgIUgIEoKEICFICBKChCAhSAgSgoQgIUgIEoKEICFILM9x3/zz/xlv0WeZkBAkBAlBQpAQJAQJQUKQECQECUFCkBAkBAlBQpAQJAQJQUKQECT+glQRUV/879wAAAAASUVORK5CYII=\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_5\">\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"202.934538\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"259.543234\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_6\">\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m4e54e57180\" y=\"27.978995\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m4e54e57180\" y=\"50.622473\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m4e54e57180\" y=\"73.265951\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_13\">\n",
       "    <path d=\"M 197.273668 90.24856 \n",
       "L 197.273668 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_14\">\n",
       "    <path d=\"M 265.204103 90.24856 \n",
       "L 265.204103 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_15\">\n",
       "    <path d=\"M 197.273668 90.24856 \n",
       "L 265.204103 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_16\">\n",
       "    <path d=\"M 197.273668 22.318125 \n",
       "L 265.204103 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_7\">\n",
       "    <!-- Head 3 -->\n",
       "    <g transform=\"translate(209.824511 16.318125)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_4\">\n",
       "   <g id=\"patch_17\">\n",
       "    <path d=\"M 278.79019 90.24856 \n",
       "L 346.720625 90.24856 \n",
       "L 346.720625 22.318125 \n",
       "L 278.79019 22.318125 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p87ccee2beb)\">\n",
       "    <image height=\"68\" id=\"imaged99c02a64a\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"278.79019\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAAyUlEQVR4nO3ZoRECMRBA0RwWSqA/KIkCKQBz+vBPXQRDxH96RebPip3JduyfY5z0vN7Pjo4xxnjt76n5FVz+/YDVFAQFQUFQEBQEBUFBUBAUBNvM6T5r5tRf5cxvQ1AQFAQFQUFQEBQEBUFBUBAUBAVBQVAQFAQFQUFQEBQEBUFBUBBsj3E7/Q2xylfBL7UhKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgICoKCoCAoCAqCgqAgKAgKgoKgICgICoKCoCD4AkosEi98EE1QAAAAAElFTkSuQmCC\" y=\"-22.24856\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_7\">\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"284.45106\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"341.059755\" xlink:href=\"#m5b4ee4c6f1\" y=\"90.24856\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_8\">\n",
       "    <g id=\"ytick_10\">\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m4e54e57180\" y=\"27.978995\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_11\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m4e54e57180\" y=\"50.622473\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_12\">\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m4e54e57180\" y=\"73.265951\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_18\">\n",
       "    <path d=\"M 278.79019 90.24856 \n",
       "L 278.79019 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_19\">\n",
       "    <path d=\"M 346.720625 90.24856 \n",
       "L 346.720625 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_20\">\n",
       "    <path d=\"M 278.79019 90.24856 \n",
       "L 346.720625 90.24856 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_21\">\n",
       "    <path d=\"M 278.79019 22.318125 \n",
       "L 346.720625 22.318125 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_8\">\n",
       "    <!-- Head 4 -->\n",
       "    <g transform=\"translate(291.341033 16.318125)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_5\">\n",
       "   <g id=\"patch_22\">\n",
       "    <path d=\"M 34.240625 194.026742 \n",
       "L 102.17106 194.026742 \n",
       "L 102.17106 126.096307 \n",
       "L 34.240625 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pa7b7ec57d7)\">\n",
       "    <image height=\"68\" id=\"image906af5f0e9\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"34.240625\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAABOElEQVR4nO3aMUoDURRA0f8TJc0QAloI9jYuw9YdZAFpkm1kAzb21lZuIFhZBgxiYyHMAtIEUiSZ9Ld6rwgGvKf+PB6XX8wMU7vNuitB3X4XPVpKKeXp5i58dtau4oN7/dQe9XIQH52a/A8YBAwCBgGDgEHAIGAQMAgYBGrq0f2wTw0/vL+Gz35P5+Gz96tlao8MbwgYBAwCBgGDgEHAIGAQMAgYBAwC9WV4HX6XGX8uctOvbuOL1JqbfSLeEDAIGAQMAgYBg4BBwCBgEDAIXPxsE38FNaPU8HN5HM/whoBBwCBgEDAIGAQMAgYBg4BBoO4+3sJf3RePk9Twh9+v9EJ/zRsCBgGDgEHAIGAQMAgYBAwCBgGDQJ2UJvwu87xpT7nLWfCGgEHAIGAQMAgYBAwCBgGDgEHgCMBZKOXHHABkAAAAAElFTkSuQmCC\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_9\">\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"39.901495\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(36.720245 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"96.51019\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(93.32894 208.625179)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_11\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(35.142561 222.303304)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 9.8125 72.90625 \n",
       "L 19.671875 72.90625 \n",
       "L 19.671875 42.09375 \n",
       "L 52.390625 72.90625 \n",
       "L 65.09375 72.90625 \n",
       "L 28.90625 38.921875 \n",
       "L 67.671875 0 \n",
       "L 54.6875 0 \n",
       "L 19.671875 35.109375 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-75\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_10\">\n",
       "    <g id=\"ytick_13\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m4e54e57180\" y=\"131.757176\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(20.878125 135.556395)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_14\">\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m4e54e57180\" y=\"154.400655\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(20.878125 158.199873)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_15\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m4e54e57180\" y=\"177.044133\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 4 -->\n",
       "      <g transform=\"translate(20.878125 180.843352)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_15\">\n",
       "     <!-- Query positions -->\n",
       "     <g transform=\"translate(14.798437 199.256055)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-81\"/>\n",
       "      <use x=\"78.710938\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"142.089844\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"203.613281\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"244.726562\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"303.90625\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"335.693359\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"399.169922\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"460.351562\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"512.451172\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"540.234375\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"579.443359\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"607.226562\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"668.408203\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"731.787109\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_23\">\n",
       "    <path d=\"M 34.240625 194.026742 \n",
       "L 34.240625 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_24\">\n",
       "    <path d=\"M 102.17106 194.026742 \n",
       "L 102.17106 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_25\">\n",
       "    <path d=\"M 34.240625 194.026742 \n",
       "L 102.17106 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_26\">\n",
       "    <path d=\"M 34.240625 126.096307 \n",
       "L 102.17106 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_16\">\n",
       "    <!-- Head 1 -->\n",
       "    <g transform=\"translate(46.791467 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_6\">\n",
       "   <g id=\"patch_27\">\n",
       "    <path d=\"M 115.757147 194.026742 \n",
       "L 183.687582 194.026742 \n",
       "L 183.687582 126.096307 \n",
       "L 115.757147 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pdfe08be505)\">\n",
       "    <image height=\"68\" id=\"imagea64cf6bee4\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"115.757147\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAABM0lEQVR4nO3boU5CURjAcQ9cEAz6HDZNJiLBxkP4GCaj70Cm0nkFizQDzOQGASy0C9dg+6fvY2PD+f/lb2dn/51wznZvqSevzUVQuRtER39d9sOj5eo6PHt4m6W20Xp4jM+mVv4HDAIGAYOAQcAgYBAwCBgEDAKl2X2Hr+5ZzeYrPDu+jT8LnlaLY7YT4gkBg4BBwCBgEDAIGAQMAgYBg4BBoBw+5+G3zPR+mFp8tHyPb6TbS619Kp4QMAgYBAwCBgGDgEHAIGAQMAiU585N+Or+sv7IrV514htptXNrn4gnBAwCBgGDgEHAIGAQMAgYBAwCVZ36fij3sdG5XMczPCFgEDAIGAQMAgYBg4BBwCBgEDAIVNt6Hx4u3fiPyX+VJwQMAgYBg4BBwCBgEDAIGAQMAj9zOyH0Eq+M7QAAAABJRU5ErkJggg==\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_11\">\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"121.418016\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_17\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(118.236766 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"178.026712\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_18\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(174.845462 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_19\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(116.659083 222.303304)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_12\">\n",
       "    <g id=\"ytick_16\">\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m4e54e57180\" y=\"131.757176\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_17\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m4e54e57180\" y=\"154.400655\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_18\">\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m4e54e57180\" y=\"177.044133\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_28\">\n",
       "    <path d=\"M 115.757147 194.026742 \n",
       "L 115.757147 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_29\">\n",
       "    <path d=\"M 183.687582 194.026742 \n",
       "L 183.687582 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_30\">\n",
       "    <path d=\"M 115.757147 194.026742 \n",
       "L 183.687582 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_31\">\n",
       "    <path d=\"M 115.757147 126.096307 \n",
       "L 183.687582 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_20\">\n",
       "    <!-- Head 2 -->\n",
       "    <g transform=\"translate(128.307989 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_7\">\n",
       "   <g id=\"patch_32\">\n",
       "    <path d=\"M 197.273668 194.026742 \n",
       "L 265.204103 194.026742 \n",
       "L 265.204103 126.096307 \n",
       "L 197.273668 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pb9552ff3f1)\">\n",
       "    <image height=\"68\" id=\"image56c2f80dfd\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"197.273668\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAABMElEQVR4nO3aMUoDURRG4fsSSZAEGxEs7JJNuJlgKu2yCu3trCT7cQOCkCpga4ohEIhjf6p7CyHi+eqfx3B4xYRJ67uvPpJer+fZaURELD8/8uNul9+OxqXnaKPz9HZQOvkfMAgYBAwCBgGDgEHAIGAQMAicVcaLu9va6d/H9PT4tEpvh4/r2nMUeEPAIGAQMAgYBAwCBgGDgEHAIGAQaJXPEH2fnkZExPPVLL1dbd7S23ZxWXqOCm8IGAQMAgYBg4BBwCBgEDAIGARKnyFaa6XD3/eH/Nm/+Dpe4Q0Bg4BBwCBgEDAIGAQMAgYBg0Dp1f1hclM6/KXblvanwBsCBgGDgEHAIGAQMAgYBAwCBgGDQLuPafpvQX/xt0mVNwQMAgYBg4BBwCBgEDAIGAQMAj/68CMv9SGwlQAAAABJRU5ErkJggg==\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_13\">\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"202.934538\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_21\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(199.753288 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"259.543234\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_22\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(256.361984 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_23\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(198.175605 222.303304)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_14\">\n",
       "    <g id=\"ytick_19\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m4e54e57180\" y=\"131.757176\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_20\">\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m4e54e57180\" y=\"154.400655\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_21\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m4e54e57180\" y=\"177.044133\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_33\">\n",
       "    <path d=\"M 197.273668 194.026742 \n",
       "L 197.273668 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_34\">\n",
       "    <path d=\"M 265.204103 194.026742 \n",
       "L 265.204103 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_35\">\n",
       "    <path d=\"M 197.273668 194.026742 \n",
       "L 265.204103 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_36\">\n",
       "    <path d=\"M 197.273668 126.096307 \n",
       "L 265.204103 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_24\">\n",
       "    <!-- Head 3 -->\n",
       "    <g transform=\"translate(209.824511 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_8\">\n",
       "   <g id=\"patch_37\">\n",
       "    <path d=\"M 278.79019 194.026742 \n",
       "L 346.720625 194.026742 \n",
       "L 346.720625 126.096307 \n",
       "L 278.79019 126.096307 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pd3554cbb36)\">\n",
       "    <image height=\"68\" id=\"image54bb391df2\" transform=\"scale(1 -1)translate(0 -68)\" width=\"68\" x=\"278.79019\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAABIElEQVR4nO3bsWnDQBSA4Tv7iCFWoz6QOTKRM0jIBoaQxiN4Co/gBUIGSCMMxpbS/9V7hUAh/1c/xPHrFYJDdfw6TyWq68OjpZRSN4/h2Wkcw7Pj6Zg6x2X/GZ5dpZ78DxgEDAIGAYOAQcAgYBAwCBgE6jT8xD/dk163T+HZj+F7rmOkuCFgEDAIGAQMAgYBg4BBwCBgEDAItOl2DQ/X9pB6eN/W4dnMNURdzfce3RAwCBgEDAIGAYOAQcAgYBAwCLTM53jmWqGU5VwtZLghYBAwCBgEDAIGAYOAQcAgYBBo98NbePj95XnGoyyDGwIGAYOAQcAgYBAwCBgEDAIGAYNA3ZUu/DfEX7xWyHJDwCBgEDAIGAQMAgYBg4BBwCDwC78OIulFgNcqAAAAAElFTkSuQmCC\" y=\"-126.026742\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_15\">\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"284.45106\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_25\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(281.26981 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"341.059755\" xlink:href=\"#m5b4ee4c6f1\" y=\"194.026742\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_26\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(337.878505 208.625179)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_27\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(279.692126 222.303304)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_16\">\n",
       "    <g id=\"ytick_22\">\n",
       "     <g id=\"line2d_38\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m4e54e57180\" y=\"131.757176\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_23\">\n",
       "     <g id=\"line2d_39\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m4e54e57180\" y=\"154.400655\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_24\">\n",
       "     <g id=\"line2d_40\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m4e54e57180\" y=\"177.044133\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_38\">\n",
       "    <path d=\"M 278.79019 194.026742 \n",
       "L 278.79019 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_39\">\n",
       "    <path d=\"M 346.720625 194.026742 \n",
       "L 346.720625 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_40\">\n",
       "    <path d=\"M 278.79019 194.026742 \n",
       "L 346.720625 194.026742 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_41\">\n",
       "    <path d=\"M 278.79019 126.096307 \n",
       "L 346.720625 126.096307 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_28\">\n",
       "    <!-- Head 4 -->\n",
       "    <g transform=\"translate(291.341033 120.096307)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_9\">\n",
       "   <g id=\"patch_42\">\n",
       "    <path clip-path=\"url(#p02fb42d84e)\" d=\"M 366.250625 165.250433 \n",
       "L 366.250625 164.804511 \n",
       "L 366.250625 51.540355 \n",
       "L 366.250625 51.094433 \n",
       "L 371.958425 51.094433 \n",
       "L 371.958425 51.540355 \n",
       "L 371.958425 164.804511 \n",
       "L 371.958425 165.250433 \n",
       "z\n",
       "\" style=\"fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;\"/>\n",
       "   </g>\n",
       "   <image height=\"114\" id=\"image1efe69578c\" transform=\"scale(1 -1)translate(0 -114)\" width=\"6\" x=\"366\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAAYAAAByCAYAAABwf6CfAAAAyElEQVR4nL2VSQ7EMAgEieT/fzWXnMYs8wHKUkcoOYK6CzCOr3rusuZbVtnFT4kMSrSIN4xihlwu9/GBwjdZYYOQqCBFyAy0QoU7KSBxOEGdMdgHzUq34vOgZcCDYqu5IU42OJfAG8XLQL+MQYZuJXdevCXYICU2MXhWKjz3XLl6wtWrlgFPUdIbFWQVpDgw2rgtx3KRIcNd7vwFAxVF023DJ4X3cVtpCAdFkCKwXBmOCmTAkhwUOBInxZ6zQsXvA8amhdOtSPEH+zQMSlnMFgMAAAAASUVORK5CYII=\" y=\"-51\"/>\n",
       "   <g id=\"matplotlib.axis_17\"/>\n",
       "   <g id=\"matplotlib.axis_18\">\n",
       "    <g id=\"ytick_25\">\n",
       "     <g id=\"line2d_41\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 3.5 0 \n",
       "\" id=\"m9a91dc340a\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#m9a91dc340a\" y=\"165.250433\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_29\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(378.958425 169.049652)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_26\">\n",
       "     <g id=\"line2d_42\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#m9a91dc340a\" y=\"142.419233\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_30\">\n",
       "      <!-- 0.2 -->\n",
       "      <g transform=\"translate(378.958425 146.218452)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_27\">\n",
       "     <g id=\"line2d_43\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#m9a91dc340a\" y=\"119.588033\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_31\">\n",
       "      <!-- 0.4 -->\n",
       "      <g transform=\"translate(378.958425 123.387252)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_28\">\n",
       "     <g id=\"line2d_44\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#m9a91dc340a\" y=\"96.756833\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_32\">\n",
       "      <!-- 0.6 -->\n",
       "      <g transform=\"translate(378.958425 100.556052)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 33.015625 40.375 \n",
       "Q 26.375 40.375 22.484375 35.828125 \n",
       "Q 18.609375 31.296875 18.609375 23.390625 \n",
       "Q 18.609375 15.53125 22.484375 10.953125 \n",
       "Q 26.375 6.390625 33.015625 6.390625 \n",
       "Q 39.65625 6.390625 43.53125 10.953125 \n",
       "Q 47.40625 15.53125 47.40625 23.390625 \n",
       "Q 47.40625 31.296875 43.53125 35.828125 \n",
       "Q 39.65625 40.375 33.015625 40.375 \n",
       "z\n",
       "M 52.59375 71.296875 \n",
       "L 52.59375 62.3125 \n",
       "Q 48.875 64.0625 45.09375 64.984375 \n",
       "Q 41.3125 65.921875 37.59375 65.921875 \n",
       "Q 27.828125 65.921875 22.671875 59.328125 \n",
       "Q 17.53125 52.734375 16.796875 39.40625 \n",
       "Q 19.671875 43.65625 24.015625 45.921875 \n",
       "Q 28.375 48.1875 33.59375 48.1875 \n",
       "Q 44.578125 48.1875 50.953125 41.515625 \n",
       "Q 57.328125 34.859375 57.328125 23.390625 \n",
       "Q 57.328125 12.15625 50.6875 5.359375 \n",
       "Q 44.046875 -1.421875 33.015625 -1.421875 \n",
       "Q 20.359375 -1.421875 13.671875 8.265625 \n",
       "Q 6.984375 17.96875 6.984375 36.375 \n",
       "Q 6.984375 53.65625 15.1875 63.9375 \n",
       "Q 23.390625 74.21875 37.203125 74.21875 \n",
       "Q 40.921875 74.21875 44.703125 73.484375 \n",
       "Q 48.484375 72.75 52.59375 71.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-54\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-54\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_29\">\n",
       "     <g id=\"line2d_45\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#m9a91dc340a\" y=\"73.925633\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_33\">\n",
       "      <!-- 0.8 -->\n",
       "      <g transform=\"translate(378.958425 77.724852)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 31.78125 34.625 \n",
       "Q 24.75 34.625 20.71875 30.859375 \n",
       "Q 16.703125 27.09375 16.703125 20.515625 \n",
       "Q 16.703125 13.921875 20.71875 10.15625 \n",
       "Q 24.75 6.390625 31.78125 6.390625 \n",
       "Q 38.8125 6.390625 42.859375 10.171875 \n",
       "Q 46.921875 13.96875 46.921875 20.515625 \n",
       "Q 46.921875 27.09375 42.890625 30.859375 \n",
       "Q 38.875 34.625 31.78125 34.625 \n",
       "z\n",
       "M 21.921875 38.8125 \n",
       "Q 15.578125 40.375 12.03125 44.71875 \n",
       "Q 8.5 49.078125 8.5 55.328125 \n",
       "Q 8.5 64.0625 14.71875 69.140625 \n",
       "Q 20.953125 74.21875 31.78125 74.21875 \n",
       "Q 42.671875 74.21875 48.875 69.140625 \n",
       "Q 55.078125 64.0625 55.078125 55.328125 \n",
       "Q 55.078125 49.078125 51.53125 44.71875 \n",
       "Q 48 40.375 41.703125 38.8125 \n",
       "Q 48.828125 37.15625 52.796875 32.3125 \n",
       "Q 56.78125 27.484375 56.78125 20.515625 \n",
       "Q 56.78125 9.90625 50.3125 4.234375 \n",
       "Q 43.84375 -1.421875 31.78125 -1.421875 \n",
       "Q 19.734375 -1.421875 13.25 4.234375 \n",
       "Q 6.78125 9.90625 6.78125 20.515625 \n",
       "Q 6.78125 27.484375 10.78125 32.3125 \n",
       "Q 14.796875 37.15625 21.921875 38.8125 \n",
       "z\n",
       "M 18.3125 54.390625 \n",
       "Q 18.3125 48.734375 21.84375 45.5625 \n",
       "Q 25.390625 42.390625 31.78125 42.390625 \n",
       "Q 38.140625 42.390625 41.71875 45.5625 \n",
       "Q 45.3125 48.734375 45.3125 54.390625 \n",
       "Q 45.3125 60.0625 41.71875 63.234375 \n",
       "Q 38.140625 66.40625 31.78125 66.40625 \n",
       "Q 25.390625 66.40625 21.84375 63.234375 \n",
       "Q 18.3125 60.0625 18.3125 54.390625 \n",
       "z\n",
       "\" id=\"DejaVuSans-56\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-56\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_30\">\n",
       "     <g id=\"line2d_46\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#m9a91dc340a\" y=\"51.094433\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_34\">\n",
       "      <!-- 1.0 -->\n",
       "      <g transform=\"translate(378.958425 54.893652)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_43\">\n",
       "    <path d=\"M 366.250625 165.250433 \n",
       "L 366.250625 164.804511 \n",
       "L 366.250625 51.540355 \n",
       "L 366.250625 51.094433 \n",
       "L 371.958425 51.094433 \n",
       "L 371.958425 51.540355 \n",
       "L 371.958425 164.804511 \n",
       "L 371.958425 165.250433 \n",
       "z\n",
       "\" style=\"fill:none;stroke:#000000;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pa7f80fb90b\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"34.240625\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p63d43f1299\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"115.757147\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p2f378f7a7d\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"197.273668\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p87ccee2beb\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"278.79019\" y=\"22.318125\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pa7b7ec57d7\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"34.240625\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pdfe08be505\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"115.757147\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pb9552ff3f1\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"197.273668\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pd3554cbb36\">\n",
       "   <rect height=\"67.930435\" width=\"67.930435\" x=\"278.79019\" y=\"126.096307\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p02fb42d84e\">\n",
       "   <rect height=\"114.156\" width=\"5.7078\" x=\"366.250625\" y=\"51.094433\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 504x252 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plusonetoincludethebeginning-of-sequencetoken\n",
    "d2l.show_heatmaps(\n",
    "    dec_self_attention_weights[:, :, :, :len(translation.split()) + 1],\n",
    "    xlabel='Key positions', ylabel='Query positions',\n",
    "    titles=['Head %d' % i for i in range(1, 5)], figsize=(7, 3.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 70
   },
   "source": [
    "与编码器的自注意力的情况类似，通过指定输入序列的有效长度，[**输出序列的查询不会与输入序列中填充位置的词元进行注意力计算**]。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "origin_pos": 71,
    "tab": [
     "pytorch"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"208.108094pt\" version=\"1.1\" viewBox=\"0 0 402.06155 208.108094\" width=\"402.06155pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2021-12-08T21:38:46.348556</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
       "     <cc:Agent>\n",
       "      <dc:title>Matplotlib v3.3.3, https://matplotlib.org/</dc:title>\n",
       "     </cc:Agent>\n",
       "    </dc:creator>\n",
       "   </cc:Work>\n",
       "  </rdf:RDF>\n",
       " </metadata>\n",
       " <defs>\n",
       "  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 208.108094 \n",
       "L 402.06155 208.108094 \n",
       "L 402.06155 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 34.240625 66.773662 \n",
       "L 102.17106 66.773662 \n",
       "L 102.17106 26.015401 \n",
       "L 34.240625 26.015401 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p3f5bfbd1de)\">\n",
       "    <image height=\"41\" id=\"imaged70a781f0f\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"34.240625\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABFUlEQVR4nO3XMUoDQRiG4fmzKUQWYhob0Quk8iApQjorGwurFF7EMnfwIqnSaQhCSJHCygQ07U76j/kgILKBvE85wyzDyw/DRvO1ysloFjO3ldLne3k9OvZI9fDiv3ci/O3PFEEEQQRBBEEEQUS8XV3bZ3e8WfqTP9/l9Y5vHHX/6Iu1hQkRBBEEEQQRBBEEEdH8bu2z+1zf2oPT/eZfLtQ2JkQQRBBEEEQQRBBERN7v7LOb3R9tSmk7GhbXe5NHe6YaPh1/s5YwIYIggiCCIIIgopuzfWRSqiq7VQ9uiut5+eG/V36YTgoTIggiCCIIIggiCCK6EWE3X+/u7d5kPS9vXFz+9U6tYkIEQQRBBEEEQQRBxAEP9SlAH8oaCAAAAABJRU5ErkJggg==\" y=\"-25.773662\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m8c3192aefd\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"37.637147\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"71.602364\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m67bf61e91e\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m67bf61e91e\" y=\"29.411923\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(20.878125 33.211141)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m67bf61e91e\" y=\"63.37714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(20.878125 67.176359)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_3\">\n",
       "     <!-- Query positions -->\n",
       "     <g transform=\"translate(14.798437 85.589063)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 39.40625 66.21875 \n",
       "Q 28.65625 66.21875 22.328125 58.203125 \n",
       "Q 16.015625 50.203125 16.015625 36.375 \n",
       "Q 16.015625 22.609375 22.328125 14.59375 \n",
       "Q 28.65625 6.59375 39.40625 6.59375 \n",
       "Q 50.140625 6.59375 56.421875 14.59375 \n",
       "Q 62.703125 22.609375 62.703125 36.375 \n",
       "Q 62.703125 50.203125 56.421875 58.203125 \n",
       "Q 50.140625 66.21875 39.40625 66.21875 \n",
       "z\n",
       "M 53.21875 1.3125 \n",
       "L 66.21875 -12.890625 \n",
       "L 54.296875 -12.890625 \n",
       "L 43.5 -1.21875 \n",
       "Q 41.890625 -1.3125 41.03125 -1.359375 \n",
       "Q 40.1875 -1.421875 39.40625 -1.421875 \n",
       "Q 24.03125 -1.421875 14.8125 8.859375 \n",
       "Q 5.609375 19.140625 5.609375 36.375 \n",
       "Q 5.609375 53.65625 14.8125 63.9375 \n",
       "Q 24.03125 74.21875 39.40625 74.21875 \n",
       "Q 54.734375 74.21875 63.90625 63.9375 \n",
       "Q 73.09375 53.65625 73.09375 36.375 \n",
       "Q 73.09375 23.6875 67.984375 14.640625 \n",
       "Q 62.890625 5.609375 53.21875 1.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-81\"/>\n",
       "       <path d=\"M 8.5 21.578125 \n",
       "L 8.5 54.6875 \n",
       "L 17.484375 54.6875 \n",
       "L 17.484375 21.921875 \n",
       "Q 17.484375 14.15625 20.5 10.265625 \n",
       "Q 23.53125 6.390625 29.59375 6.390625 \n",
       "Q 36.859375 6.390625 41.078125 11.03125 \n",
       "Q 45.3125 15.671875 45.3125 23.6875 \n",
       "L 45.3125 54.6875 \n",
       "L 54.296875 54.6875 \n",
       "L 54.296875 0 \n",
       "L 45.3125 0 \n",
       "L 45.3125 8.40625 \n",
       "Q 42.046875 3.421875 37.71875 1 \n",
       "Q 33.40625 -1.421875 27.6875 -1.421875 \n",
       "Q 18.265625 -1.421875 13.375 4.4375 \n",
       "Q 8.5 10.296875 8.5 21.578125 \n",
       "z\n",
       "M 31.109375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-117\"/>\n",
       "       <path d=\"M 56.203125 29.59375 \n",
       "L 56.203125 25.203125 \n",
       "L 14.890625 25.203125 \n",
       "Q 15.484375 15.921875 20.484375 11.0625 \n",
       "Q 25.484375 6.203125 34.421875 6.203125 \n",
       "Q 39.59375 6.203125 44.453125 7.46875 \n",
       "Q 49.3125 8.734375 54.109375 11.28125 \n",
       "L 54.109375 2.78125 \n",
       "Q 49.265625 0.734375 44.1875 -0.34375 \n",
       "Q 39.109375 -1.421875 33.890625 -1.421875 \n",
       "Q 20.796875 -1.421875 13.15625 6.1875 \n",
       "Q 5.515625 13.8125 5.515625 26.8125 \n",
       "Q 5.515625 40.234375 12.765625 48.109375 \n",
       "Q 20.015625 56 32.328125 56 \n",
       "Q 43.359375 56 49.78125 48.890625 \n",
       "Q 56.203125 41.796875 56.203125 29.59375 \n",
       "z\n",
       "M 47.21875 32.234375 \n",
       "Q 47.125 39.59375 43.09375 43.984375 \n",
       "Q 39.0625 48.390625 32.421875 48.390625 \n",
       "Q 24.90625 48.390625 20.390625 44.140625 \n",
       "Q 15.875 39.890625 15.1875 32.171875 \n",
       "z\n",
       "\" id=\"DejaVuSans-101\"/>\n",
       "       <path d=\"M 41.109375 46.296875 \n",
       "Q 39.59375 47.171875 37.8125 47.578125 \n",
       "Q 36.03125 48 33.890625 48 \n",
       "Q 26.265625 48 22.1875 43.046875 \n",
       "Q 18.109375 38.09375 18.109375 28.8125 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 20.953125 51.171875 25.484375 53.578125 \n",
       "Q 30.03125 56 36.53125 56 \n",
       "Q 37.453125 56 38.578125 55.875 \n",
       "Q 39.703125 55.765625 41.0625 55.515625 \n",
       "z\n",
       "\" id=\"DejaVuSans-114\"/>\n",
       "       <path d=\"M 32.171875 -5.078125 \n",
       "Q 28.375 -14.84375 24.75 -17.8125 \n",
       "Q 21.140625 -20.796875 15.09375 -20.796875 \n",
       "L 7.90625 -20.796875 \n",
       "L 7.90625 -13.28125 \n",
       "L 13.1875 -13.28125 \n",
       "Q 16.890625 -13.28125 18.9375 -11.515625 \n",
       "Q 21 -9.765625 23.484375 -3.21875 \n",
       "L 25.09375 0.875 \n",
       "L 2.984375 54.6875 \n",
       "L 12.5 54.6875 \n",
       "L 29.59375 11.921875 \n",
       "L 46.6875 54.6875 \n",
       "L 56.203125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-121\"/>\n",
       "       <path id=\"DejaVuSans-32\"/>\n",
       "       <path d=\"M 18.109375 8.203125 \n",
       "L 18.109375 -20.796875 \n",
       "L 9.078125 -20.796875 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.390625 \n",
       "Q 20.953125 51.265625 25.265625 53.625 \n",
       "Q 29.59375 56 35.59375 56 \n",
       "Q 45.5625 56 51.78125 48.09375 \n",
       "Q 58.015625 40.1875 58.015625 27.296875 \n",
       "Q 58.015625 14.40625 51.78125 6.484375 \n",
       "Q 45.5625 -1.421875 35.59375 -1.421875 \n",
       "Q 29.59375 -1.421875 25.265625 0.953125 \n",
       "Q 20.953125 3.328125 18.109375 8.203125 \n",
       "z\n",
       "M 48.6875 27.296875 \n",
       "Q 48.6875 37.203125 44.609375 42.84375 \n",
       "Q 40.53125 48.484375 33.40625 48.484375 \n",
       "Q 26.265625 48.484375 22.1875 42.84375 \n",
       "Q 18.109375 37.203125 18.109375 27.296875 \n",
       "Q 18.109375 17.390625 22.1875 11.75 \n",
       "Q 26.265625 6.109375 33.40625 6.109375 \n",
       "Q 40.53125 6.109375 44.609375 11.75 \n",
       "Q 48.6875 17.390625 48.6875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-112\"/>\n",
       "       <path d=\"M 30.609375 48.390625 \n",
       "Q 23.390625 48.390625 19.1875 42.75 \n",
       "Q 14.984375 37.109375 14.984375 27.296875 \n",
       "Q 14.984375 17.484375 19.15625 11.84375 \n",
       "Q 23.34375 6.203125 30.609375 6.203125 \n",
       "Q 37.796875 6.203125 41.984375 11.859375 \n",
       "Q 46.1875 17.53125 46.1875 27.296875 \n",
       "Q 46.1875 37.015625 41.984375 42.703125 \n",
       "Q 37.796875 48.390625 30.609375 48.390625 \n",
       "z\n",
       "M 30.609375 56 \n",
       "Q 42.328125 56 49.015625 48.375 \n",
       "Q 55.71875 40.765625 55.71875 27.296875 \n",
       "Q 55.71875 13.875 49.015625 6.21875 \n",
       "Q 42.328125 -1.421875 30.609375 -1.421875 \n",
       "Q 18.84375 -1.421875 12.171875 6.21875 \n",
       "Q 5.515625 13.875 5.515625 27.296875 \n",
       "Q 5.515625 40.765625 12.171875 48.375 \n",
       "Q 18.84375 56 30.609375 56 \n",
       "z\n",
       "\" id=\"DejaVuSans-111\"/>\n",
       "       <path d=\"M 44.28125 53.078125 \n",
       "L 44.28125 44.578125 \n",
       "Q 40.484375 46.53125 36.375 47.5 \n",
       "Q 32.28125 48.484375 27.875 48.484375 \n",
       "Q 21.1875 48.484375 17.84375 46.4375 \n",
       "Q 14.5 44.390625 14.5 40.28125 \n",
       "Q 14.5 37.15625 16.890625 35.375 \n",
       "Q 19.28125 33.59375 26.515625 31.984375 \n",
       "L 29.59375 31.296875 \n",
       "Q 39.15625 29.25 43.1875 25.515625 \n",
       "Q 47.21875 21.78125 47.21875 15.09375 \n",
       "Q 47.21875 7.46875 41.1875 3.015625 \n",
       "Q 35.15625 -1.421875 24.609375 -1.421875 \n",
       "Q 20.21875 -1.421875 15.453125 -0.5625 \n",
       "Q 10.6875 0.296875 5.421875 2 \n",
       "L 5.421875 11.28125 \n",
       "Q 10.40625 8.6875 15.234375 7.390625 \n",
       "Q 20.0625 6.109375 24.8125 6.109375 \n",
       "Q 31.15625 6.109375 34.5625 8.28125 \n",
       "Q 37.984375 10.453125 37.984375 14.40625 \n",
       "Q 37.984375 18.0625 35.515625 20.015625 \n",
       "Q 33.0625 21.96875 24.703125 23.78125 \n",
       "L 21.578125 24.515625 \n",
       "Q 13.234375 26.265625 9.515625 29.90625 \n",
       "Q 5.8125 33.546875 5.8125 39.890625 \n",
       "Q 5.8125 47.609375 11.28125 51.796875 \n",
       "Q 16.75 56 26.8125 56 \n",
       "Q 31.78125 56 36.171875 55.265625 \n",
       "Q 40.578125 54.546875 44.28125 53.078125 \n",
       "z\n",
       "\" id=\"DejaVuSans-115\"/>\n",
       "       <path d=\"M 9.421875 54.6875 \n",
       "L 18.40625 54.6875 \n",
       "L 18.40625 0 \n",
       "L 9.421875 0 \n",
       "z\n",
       "M 9.421875 75.984375 \n",
       "L 18.40625 75.984375 \n",
       "L 18.40625 64.59375 \n",
       "L 9.421875 64.59375 \n",
       "z\n",
       "\" id=\"DejaVuSans-105\"/>\n",
       "       <path d=\"M 18.3125 70.21875 \n",
       "L 18.3125 54.6875 \n",
       "L 36.8125 54.6875 \n",
       "L 36.8125 47.703125 \n",
       "L 18.3125 47.703125 \n",
       "L 18.3125 18.015625 \n",
       "Q 18.3125 11.328125 20.140625 9.421875 \n",
       "Q 21.96875 7.515625 27.59375 7.515625 \n",
       "L 36.8125 7.515625 \n",
       "L 36.8125 0 \n",
       "L 27.59375 0 \n",
       "Q 17.1875 0 13.234375 3.875 \n",
       "Q 9.28125 7.765625 9.28125 18.015625 \n",
       "L 9.28125 47.703125 \n",
       "L 2.6875 47.703125 \n",
       "L 2.6875 54.6875 \n",
       "L 9.28125 54.6875 \n",
       "L 9.28125 70.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-116\"/>\n",
       "       <path d=\"M 54.890625 33.015625 \n",
       "L 54.890625 0 \n",
       "L 45.90625 0 \n",
       "L 45.90625 32.71875 \n",
       "Q 45.90625 40.484375 42.875 44.328125 \n",
       "Q 39.84375 48.1875 33.796875 48.1875 \n",
       "Q 26.515625 48.1875 22.3125 43.546875 \n",
       "Q 18.109375 38.921875 18.109375 30.90625 \n",
       "L 18.109375 0 \n",
       "L 9.078125 0 \n",
       "L 9.078125 54.6875 \n",
       "L 18.109375 54.6875 \n",
       "L 18.109375 46.1875 \n",
       "Q 21.34375 51.125 25.703125 53.5625 \n",
       "Q 30.078125 56 35.796875 56 \n",
       "Q 45.21875 56 50.046875 50.171875 \n",
       "Q 54.890625 44.34375 54.890625 33.015625 \n",
       "z\n",
       "\" id=\"DejaVuSans-110\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-81\"/>\n",
       "      <use x=\"78.710938\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"142.089844\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"203.613281\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"244.726562\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"303.90625\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"335.693359\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"399.169922\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"460.351562\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"512.451172\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"540.234375\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"579.443359\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"607.226562\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"668.408203\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"731.787109\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 34.240625 66.773662 \n",
       "L 34.240625 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 102.17106 66.773662 \n",
       "L 102.17106 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 34.240625 66.773662 \n",
       "L 102.17106 66.773662 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 34.240625 26.015401 \n",
       "L 102.17106 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_4\">\n",
       "    <!-- Head 1 -->\n",
       "    <g transform=\"translate(46.791467 20.015401)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 9.8125 72.90625 \n",
       "L 19.671875 72.90625 \n",
       "L 19.671875 43.015625 \n",
       "L 55.515625 43.015625 \n",
       "L 55.515625 72.90625 \n",
       "L 65.375 72.90625 \n",
       "L 65.375 0 \n",
       "L 55.515625 0 \n",
       "L 55.515625 34.71875 \n",
       "L 19.671875 34.71875 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-72\"/>\n",
       "      <path d=\"M 34.28125 27.484375 \n",
       "Q 23.390625 27.484375 19.1875 25 \n",
       "Q 14.984375 22.515625 14.984375 16.5 \n",
       "Q 14.984375 11.71875 18.140625 8.90625 \n",
       "Q 21.296875 6.109375 26.703125 6.109375 \n",
       "Q 34.1875 6.109375 38.703125 11.40625 \n",
       "Q 43.21875 16.703125 43.21875 25.484375 \n",
       "L 43.21875 27.484375 \n",
       "z\n",
       "M 52.203125 31.203125 \n",
       "L 52.203125 0 \n",
       "L 43.21875 0 \n",
       "L 43.21875 8.296875 \n",
       "Q 40.140625 3.328125 35.546875 0.953125 \n",
       "Q 30.953125 -1.421875 24.3125 -1.421875 \n",
       "Q 15.921875 -1.421875 10.953125 3.296875 \n",
       "Q 6 8.015625 6 15.921875 \n",
       "Q 6 25.140625 12.171875 29.828125 \n",
       "Q 18.359375 34.515625 30.609375 34.515625 \n",
       "L 43.21875 34.515625 \n",
       "L 43.21875 35.40625 \n",
       "Q 43.21875 41.609375 39.140625 45 \n",
       "Q 35.0625 48.390625 27.6875 48.390625 \n",
       "Q 23 48.390625 18.546875 47.265625 \n",
       "Q 14.109375 46.140625 10.015625 43.890625 \n",
       "L 10.015625 52.203125 \n",
       "Q 14.9375 54.109375 19.578125 55.046875 \n",
       "Q 24.21875 56 28.609375 56 \n",
       "Q 40.484375 56 46.34375 49.84375 \n",
       "Q 52.203125 43.703125 52.203125 31.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-97\"/>\n",
       "      <path d=\"M 45.40625 46.390625 \n",
       "L 45.40625 75.984375 \n",
       "L 54.390625 75.984375 \n",
       "L 54.390625 0 \n",
       "L 45.40625 0 \n",
       "L 45.40625 8.203125 \n",
       "Q 42.578125 3.328125 38.25 0.953125 \n",
       "Q 33.9375 -1.421875 27.875 -1.421875 \n",
       "Q 17.96875 -1.421875 11.734375 6.484375 \n",
       "Q 5.515625 14.40625 5.515625 27.296875 \n",
       "Q 5.515625 40.1875 11.734375 48.09375 \n",
       "Q 17.96875 56 27.875 56 \n",
       "Q 33.9375 56 38.25 53.625 \n",
       "Q 42.578125 51.265625 45.40625 46.390625 \n",
       "z\n",
       "M 14.796875 27.296875 \n",
       "Q 14.796875 17.390625 18.875 11.75 \n",
       "Q 22.953125 6.109375 30.078125 6.109375 \n",
       "Q 37.203125 6.109375 41.296875 11.75 \n",
       "Q 45.40625 17.390625 45.40625 27.296875 \n",
       "Q 45.40625 37.203125 41.296875 42.84375 \n",
       "Q 37.203125 48.484375 30.078125 48.484375 \n",
       "Q 22.953125 48.484375 18.875 42.84375 \n",
       "Q 14.796875 37.203125 14.796875 27.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-100\"/>\n",
       "      <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_2\">\n",
       "   <g id=\"patch_7\">\n",
       "    <path d=\"M 115.757147 66.773662 \n",
       "L 183.687582 66.773662 \n",
       "L 183.687582 26.015401 \n",
       "L 115.757147 26.015401 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pc347013f1f)\">\n",
       "    <image height=\"41\" id=\"image4148aaaf99\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"115.757147\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABEklEQVR4nO3ZMUoDQRSA4cxmwcIqWNlISFAIooV9uhiwTu0VLLyBB/AQNpbp03gCC0sbS7ESBAkiImv/M29RRGeL/yv3MeHxM7CETc36pekFmiYc9W7HB9nnR1cX4Zn+dBHOuqIqvUDXGAQMAgYBg4BBoG6dfn6Eo929QX7wcB//3vQ7K5XlDQGDgEHAIGAQMAik1dZ2+Jd2dnMdHxzu5wdV/CZPVff7d3/Df2YQMAgYBAwCBoF6+fwaDo9Hh+EsVf2/2Kc4bwgYBAwCBgGDQGr9lPkWv4Hez06zz+vJODxTn1/+YLUyvCFgEDAIGAQMAgaB9k+ZG5vh6OnuMft852T+q4VK84aAQcAgYBAwCBgEvgAbASLJ/ktQxwAAAABJRU5ErkJggg==\" y=\"-25.773662\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_3\">\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"119.153668\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"153.118886\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_4\">\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m67bf61e91e\" y=\"29.411923\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m67bf61e91e\" y=\"63.37714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_8\">\n",
       "    <path d=\"M 115.757147 66.773662 \n",
       "L 115.757147 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_9\">\n",
       "    <path d=\"M 183.687582 66.773662 \n",
       "L 183.687582 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_10\">\n",
       "    <path d=\"M 115.757147 66.773662 \n",
       "L 183.687582 66.773662 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_11\">\n",
       "    <path d=\"M 115.757147 26.015401 \n",
       "L 183.687582 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_5\">\n",
       "    <!-- Head 2 -->\n",
       "    <g transform=\"translate(128.307989 20.015401)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_3\">\n",
       "   <g id=\"patch_12\">\n",
       "    <path d=\"M 197.273668 66.773662 \n",
       "L 265.204103 66.773662 \n",
       "L 265.204103 26.015401 \n",
       "L 197.273668 26.015401 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#padfb59dc68)\">\n",
       "    <image height=\"41\" id=\"image354a253b99\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"197.273668\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABA0lEQVR4nO3XPUpDQRRA4czLQwISSCOIfdqAnZuwzwIkRbBObyFYu4Q0tu4h2NuITQqXIIJg/pj0h3cfAZEJcr4yl0uGw8DwUv7+zJ3A9n4ajTppdNk8ODsPd7pX1+HsWFSlD3BsDAIGAYOAQcAgUO/mD+GwupmFs7x8bR5s1r88UlneEDAIGAQMAgYBg0Bq+9p9uhiGi+O3RfPgdBD/2Unv4IOV4g0Bg4BBwCBgEDAItD67u5fneHP53vhzXv2EK/Xk7uCDleINAYOAQcAgYBBIt6kfvjKPXx/xYtX9i/MU5w0Bg4BBwCBgEDAI1Jscvrr/9mlt4w0Bg4BBwCBgEDAI7AG13CiB2U8SdwAAAABJRU5ErkJggg==\" y=\"-25.773662\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_5\">\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"200.67019\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"234.635408\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_6\">\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m67bf61e91e\" y=\"29.411923\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m67bf61e91e\" y=\"63.37714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_13\">\n",
       "    <path d=\"M 197.273668 66.773662 \n",
       "L 197.273668 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_14\">\n",
       "    <path d=\"M 265.204103 66.773662 \n",
       "L 265.204103 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_15\">\n",
       "    <path d=\"M 197.273668 66.773662 \n",
       "L 265.204103 66.773662 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_16\">\n",
       "    <path d=\"M 197.273668 26.015401 \n",
       "L 265.204103 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_6\">\n",
       "    <!-- Head 3 -->\n",
       "    <g transform=\"translate(209.824511 20.015401)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_4\">\n",
       "   <g id=\"patch_17\">\n",
       "    <path d=\"M 278.79019 66.773662 \n",
       "L 346.720625 66.773662 \n",
       "L 346.720625 26.015401 \n",
       "L 278.79019 26.015401 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pce7eab1a31)\">\n",
       "    <image height=\"41\" id=\"imageefb43a912f\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"278.79019\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABEElEQVR4nO3ZsUrDUBhA4XttNzO0OLSTm7PQqU8gOIj6Bm5Chz6HLyD6BB37KA5OLuKgex0aRMWk+yG/FMEmw/nGXP70crgQkuaf54c6BarFbbSU8sll88J6Fc70pmfhWlfstb2BrjEIGAQMAgYBg0BeDkfhY/fi5TGe/Ppovh7eLaVcDLbcVns8IWAQMAgYBAwCBoFcrVfhg3JWHIaDd+Xrv2yobZ4QMAgYBAwCBgGDQD/VVbh4frAfrtXRx+Tvz3AmD8dbb6wtnhAwCBgEDAIGgXydivDl7r582+VeOsETAgYBg4BBwCBgEMh1+f7Ln4+xp+NJ4/Wjm3k40zu9+stP7ZQnBAwCBgGDgEHAILABrPUpKS/cOK4AAAAASUVORK5CYII=\" y=\"-25.773662\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_7\">\n",
       "    <g id=\"xtick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.186712\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"316.151929\" xlink:href=\"#m8c3192aefd\" y=\"66.773662\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_8\">\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m67bf61e91e\" y=\"29.411923\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_16\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m67bf61e91e\" y=\"63.37714\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_18\">\n",
       "    <path d=\"M 278.79019 66.773662 \n",
       "L 278.79019 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_19\">\n",
       "    <path d=\"M 346.720625 66.773662 \n",
       "L 346.720625 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_20\">\n",
       "    <path d=\"M 278.79019 66.773662 \n",
       "L 346.720625 66.773662 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_21\">\n",
       "    <path d=\"M 278.79019 26.015401 \n",
       "L 346.720625 26.015401 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_7\">\n",
       "    <!-- Head 4 -->\n",
       "    <g transform=\"translate(291.341033 20.015401)scale(0.12 -0.12)\">\n",
       "     <defs>\n",
       "      <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "     </defs>\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_5\">\n",
       "   <g id=\"patch_22\">\n",
       "    <path d=\"M 34.240625 170.551844 \n",
       "L 102.17106 170.551844 \n",
       "L 102.17106 129.793583 \n",
       "L 34.240625 129.793583 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#pb75e23d778)\">\n",
       "    <image height=\"41\" id=\"image17b8c04146\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"34.240625\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABFklEQVR4nO3XMWoCQRiG4R13IcRACgsb7VPYpcw9vIBVRGxscgG7kMYmJwi5gV0Ei9jmBja2hli4ICQ46T/2kyyCa+B9yh3+3eFlYNjw/TiIiZH2x24p2b+9Fi98fdqZtDu0a+eiVvUGzg1BBEEEQQRBBEFElk/f7eJ1L/eTzVbh43Bze+yeKsUJEQQRBBEEEQQRBBHh6bJh/3ZH66UdjLuteaNvHC7qf99ZRTghgiCCIIIggiCCICLEfGOv3furth183q7KfyyE0jOnxgkRBBEEEQQRBBHZocU0OXArRHs5edwy/w9BBEEEQQRBBEFE+Jm92Puz1rmzg/uPWeHzuJjbmexhUmJr1eCECIIIggiCCIIIgohf2q8nQ4sycwYAAAAASUVORK5CYII=\" y=\"-129.551844\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_9\">\n",
       "    <g id=\"xtick_9\">\n",
       "     <g id=\"line2d_17\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"37.637147\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(34.455897 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_10\">\n",
       "     <g id=\"line2d_18\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"71.602364\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(68.421114 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_10\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(35.142561 198.828406)scale(0.1 -0.1)\">\n",
       "      <defs>\n",
       "       <path d=\"M 9.8125 72.90625 \n",
       "L 19.671875 72.90625 \n",
       "L 19.671875 42.09375 \n",
       "L 52.390625 72.90625 \n",
       "L 65.09375 72.90625 \n",
       "L 28.90625 38.921875 \n",
       "L 67.671875 0 \n",
       "L 54.6875 0 \n",
       "L 19.671875 35.109375 \n",
       "L 19.671875 0 \n",
       "L 9.8125 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-75\"/>\n",
       "      </defs>\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_10\">\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_19\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m67bf61e91e\" y=\"133.190104\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(20.878125 136.989323)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_10\">\n",
       "     <g id=\"line2d_20\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"34.240625\" xlink:href=\"#m67bf61e91e\" y=\"167.155322\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(20.878125 170.954541)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- Query positions -->\n",
       "     <g transform=\"translate(14.798437 189.367244)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-81\"/>\n",
       "      <use x=\"78.710938\" xlink:href=\"#DejaVuSans-117\"/>\n",
       "      <use x=\"142.089844\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"203.613281\" xlink:href=\"#DejaVuSans-114\"/>\n",
       "      <use x=\"244.726562\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"303.90625\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"335.693359\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"399.169922\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"460.351562\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"512.451172\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"540.234375\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"579.443359\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"607.226562\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"668.408203\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"731.787109\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_23\">\n",
       "    <path d=\"M 34.240625 170.551844 \n",
       "L 34.240625 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_24\">\n",
       "    <path d=\"M 102.17106 170.551844 \n",
       "L 102.17106 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_25\">\n",
       "    <path d=\"M 34.240625 170.551844 \n",
       "L 102.17106 170.551844 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_26\">\n",
       "    <path d=\"M 34.240625 129.793583 \n",
       "L 102.17106 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_14\">\n",
       "    <!-- Head 1 -->\n",
       "    <g transform=\"translate(46.791467 123.793583)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_6\">\n",
       "   <g id=\"patch_27\">\n",
       "    <path d=\"M 115.757147 170.551844 \n",
       "L 183.687582 170.551844 \n",
       "L 183.687582 129.793583 \n",
       "L 115.757147 129.793583 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p56431db50b)\">\n",
       "    <image height=\"41\" id=\"imagea429f95f8b\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"115.757147\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABDklEQVR4nO3YP0oDQRhA8Z1lG/8UqcVqCeIBrC1E72Jt7w1yAAs9hCewsZAcQSSksLBQCMgWGpNJ/9hPRImT4v3K+Zjd4TGwsOnpcJirQHt/F42qav7Ru5xfpuGW+uAoft6GqEsfYNMYBAwCBgGDgEGgmbx24bBdLuKdddO7nPaGfz1TUd4QMAgYBAwCBgGDQHNycxkOJ8en4awdP6zjPMV5Q8AgYBAwCBgEDAIpd7PwJ/P5zn648ap7XsuBSvOGgEHAIGAQMAg0+eszHJ4NtsNZ7mbBIH5Z2h387FQFeUPAIGAQMAgYBAwCafn+9s2HMrYYXfSuzx+n4Z6t69vfvOpfeUPAIGAQMAgYBAwCK/+1KuTPXHPWAAAAAElFTkSuQmCC\" y=\"-129.551844\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_11\">\n",
       "    <g id=\"xtick_11\">\n",
       "     <g id=\"line2d_21\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"119.153668\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(115.972418 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_12\">\n",
       "     <g id=\"line2d_22\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"153.118886\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(149.937636 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_17\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(116.659083 198.828406)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_12\">\n",
       "    <g id=\"ytick_11\">\n",
       "     <g id=\"line2d_23\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m67bf61e91e\" y=\"133.190104\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_12\">\n",
       "     <g id=\"line2d_24\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"115.757147\" xlink:href=\"#m67bf61e91e\" y=\"167.155322\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_28\">\n",
       "    <path d=\"M 115.757147 170.551844 \n",
       "L 115.757147 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_29\">\n",
       "    <path d=\"M 183.687582 170.551844 \n",
       "L 183.687582 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_30\">\n",
       "    <path d=\"M 115.757147 170.551844 \n",
       "L 183.687582 170.551844 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_31\">\n",
       "    <path d=\"M 115.757147 129.793583 \n",
       "L 183.687582 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_18\">\n",
       "    <!-- Head 2 -->\n",
       "    <g transform=\"translate(128.307989 123.793583)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_7\">\n",
       "   <g id=\"patch_32\">\n",
       "    <path d=\"M 197.273668 170.551844 \n",
       "L 265.204103 170.551844 \n",
       "L 265.204103 129.793583 \n",
       "L 197.273668 129.793583 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p6457d19a6d)\">\n",
       "    <image height=\"41\" id=\"image27de120174\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"197.273668\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABEElEQVR4nO3ZMUoDQRSA4RldJGBSCGJhYSNWabyLF0jnBey8gr2ll/Akgo2IIFG0SFiwCQjO2v/skyyBjMX/lft47PAzEMjm0n50KVDu76JRSl9tPAvszq4H72zbTu0D/DcGAYOAQcAgYBBo/hp2b6/hLE8m/YOT040OVJs3BAwCBgGDgEHAINCk8hMO8/Q8nHVPj/0785dNz1SVNwQMAgYBg4BBwCCQy2Ie/sl8dTQNF2/a5/5BKfHL9kbrn6wSbwgYBAwCBgGDQL5M4/BX5vbzId4cHwx/Wc6Dd7bNGwIGAYOAQcAgYBBoLg6DT5IppTTaj2fL997H3fcqXMnHZ+ueqxpvCBgEDAIGAYOAQeAX0QUlb4GyvJIAAAAASUVORK5CYII=\" y=\"-129.551844\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_13\">\n",
       "    <g id=\"xtick_13\">\n",
       "     <g id=\"line2d_25\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"200.67019\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_19\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(197.48894 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_14\">\n",
       "     <g id=\"line2d_26\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"234.635408\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_20\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(231.454158 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_21\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(198.175605 198.828406)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_14\">\n",
       "    <g id=\"ytick_13\">\n",
       "     <g id=\"line2d_27\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m67bf61e91e\" y=\"133.190104\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_14\">\n",
       "     <g id=\"line2d_28\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"197.273668\" xlink:href=\"#m67bf61e91e\" y=\"167.155322\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_33\">\n",
       "    <path d=\"M 197.273668 170.551844 \n",
       "L 197.273668 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_34\">\n",
       "    <path d=\"M 265.204103 170.551844 \n",
       "L 265.204103 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_35\">\n",
       "    <path d=\"M 197.273668 170.551844 \n",
       "L 265.204103 170.551844 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_36\">\n",
       "    <path d=\"M 197.273668 129.793583 \n",
       "L 265.204103 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_22\">\n",
       "    <!-- Head 3 -->\n",
       "    <g transform=\"translate(209.824511 123.793583)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_8\">\n",
       "   <g id=\"patch_37\">\n",
       "    <path d=\"M 278.79019 170.551844 \n",
       "L 346.720625 170.551844 \n",
       "L 346.720625 129.793583 \n",
       "L 278.79019 129.793583 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g clip-path=\"url(#p0bd0da9809)\">\n",
       "    <image height=\"41\" id=\"image64b96bb39a\" transform=\"scale(1 -1)translate(0 -41)\" width=\"68\" x=\"278.79019\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAEQAAAApCAYAAACMeY82AAABGklEQVR4nO3XsWrCUBiGYY9JdClF6Vi8C8eCdPIG6kU4OArddOotFNy8C4eupTiUUrrYxbHgpIJOVtP9JV+RDCbD94w5/DmHlwMh4TDspRUhGozVUuX0/Z69UKvLmajdlWtlUS36AGXjIOAg4CDgIOAgEIe7+3yTy0X28+tG7sOUgW8IOAg4CDgIOAg4CISnelP+7T7+fOnJaizeGPRmif4TLgvfEHAQcBBwEHAQcBAIp91afnb7Vy05+LxdqlfqzeLk7IMVxTcEHAQcBBwEHARCut/Ir8x/fiejzOer6UzO3L7O82x1Ub4h4CDgIOAg4CDgIBCOHy/ys5t+vunJ5k3286QmR6LOw9kHK4pvCDgIOAg4CDgIOAj8AXQDJRExWrHeAAAAAElFTkSuQmCC\" y=\"-129.551844\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_15\">\n",
       "    <g id=\"xtick_15\">\n",
       "     <g id=\"line2d_29\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"282.186712\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_23\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(279.005462 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_16\">\n",
       "     <g id=\"line2d_30\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"316.151929\" xlink:href=\"#m8c3192aefd\" y=\"170.551844\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_24\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(312.970679 185.150281)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_25\">\n",
       "     <!-- Key positions -->\n",
       "     <g transform=\"translate(279.692126 198.828406)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-75\"/>\n",
       "      <use x=\"60.576172\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "      <use x=\"122.099609\" xlink:href=\"#DejaVuSans-121\"/>\n",
       "      <use x=\"181.279297\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "      <use x=\"213.066406\" xlink:href=\"#DejaVuSans-112\"/>\n",
       "      <use x=\"276.542969\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"337.724609\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "      <use x=\"389.824219\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"417.607422\" xlink:href=\"#DejaVuSans-116\"/>\n",
       "      <use x=\"456.816406\" xlink:href=\"#DejaVuSans-105\"/>\n",
       "      <use x=\"484.599609\" xlink:href=\"#DejaVuSans-111\"/>\n",
       "      <use x=\"545.78125\" xlink:href=\"#DejaVuSans-110\"/>\n",
       "      <use x=\"609.160156\" xlink:href=\"#DejaVuSans-115\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_16\">\n",
       "    <g id=\"ytick_15\">\n",
       "     <g id=\"line2d_31\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m67bf61e91e\" y=\"133.190104\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_16\">\n",
       "     <g id=\"line2d_32\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.79019\" xlink:href=\"#m67bf61e91e\" y=\"167.155322\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_38\">\n",
       "    <path d=\"M 278.79019 170.551844 \n",
       "L 278.79019 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_39\">\n",
       "    <path d=\"M 346.720625 170.551844 \n",
       "L 346.720625 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_40\">\n",
       "    <path d=\"M 278.79019 170.551844 \n",
       "L 346.720625 170.551844 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_41\">\n",
       "    <path d=\"M 278.79019 129.793583 \n",
       "L 346.720625 129.793583 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"text_26\">\n",
       "    <!-- Head 4 -->\n",
       "    <g transform=\"translate(291.341033 123.793583)scale(0.12 -0.12)\">\n",
       "     <use xlink:href=\"#DejaVuSans-72\"/>\n",
       "     <use x=\"75.195312\" xlink:href=\"#DejaVuSans-101\"/>\n",
       "     <use x=\"136.71875\" xlink:href=\"#DejaVuSans-97\"/>\n",
       "     <use x=\"197.998047\" xlink:href=\"#DejaVuSans-100\"/>\n",
       "     <use x=\"261.474609\" xlink:href=\"#DejaVuSans-32\"/>\n",
       "     <use x=\"293.261719\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       "  <g id=\"axes_9\">\n",
       "   <g id=\"patch_42\">\n",
       "    <path clip-path=\"url(#p2d197f1df0)\" d=\"M 366.250625 155.361622 \n",
       "L 366.250625 154.9157 \n",
       "L 366.250625 41.651544 \n",
       "L 366.250625 41.205622 \n",
       "L 371.958425 41.205622 \n",
       "L 371.958425 41.651544 \n",
       "L 371.958425 154.9157 \n",
       "L 371.958425 155.361622 \n",
       "z\n",
       "\" style=\"fill:#ffffff;stroke:#ffffff;stroke-linejoin:miter;stroke-width:0.01;\"/>\n",
       "   </g>\n",
       "   <image height=\"114\" id=\"imageb758ecb6a1\" transform=\"scale(1 -1)translate(0 -114)\" width=\"6\" x=\"366\" xlink:href=\"data:image/png;base64,\n",
       "iVBORw0KGgoAAAANSUhEUgAAAAYAAAByCAYAAABwf6CfAAAA1ElEQVR4nMWWQQ7DMAgEtxL/f2pPPTmA+wGm0lqWmmPQ7rAYR3ntz3treEJd03uFuqGwRyeFNimIsZlxr8AB7RxYqKQCwnEkpMjHtPLhKmKQFbf71xx57TxYgYybOdzzOIHTUh8MEe+HP0Sw2hdz+O0ezApz2IWkO0iKAzgz4GPpw/vBFaWueBmgUAntNn30sVCooJEUFmw4MhKn6zNmJ0UmMWaBounXAGIoSqigdg+sSIGMWfAjYNpWCJ9vhxQLV5QCYldwPRTLDohWqFj2efgMW/EF6RMLSODdIsQAAAAASUVORK5CYII=\" y=\"-41\"/>\n",
       "   <g id=\"matplotlib.axis_17\"/>\n",
       "   <g id=\"matplotlib.axis_18\">\n",
       "    <g id=\"ytick_17\">\n",
       "     <g id=\"line2d_33\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 3.5 0 \n",
       "\" id=\"mf53236dc49\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#mf53236dc49\" y=\"155.361622\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_27\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(378.958425 159.160841)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_18\">\n",
       "     <g id=\"line2d_34\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#mf53236dc49\" y=\"131.389777\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_28\">\n",
       "      <!-- 0.2 -->\n",
       "      <g transform=\"translate(378.958425 135.188996)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_19\">\n",
       "     <g id=\"line2d_35\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#mf53236dc49\" y=\"107.417933\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_29\">\n",
       "      <!-- 0.4 -->\n",
       "      <g transform=\"translate(378.958425 111.217151)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_20\">\n",
       "     <g id=\"line2d_36\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#mf53236dc49\" y=\"83.446088\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_30\">\n",
       "      <!-- 0.6 -->\n",
       "      <g transform=\"translate(378.958425 87.245307)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 33.015625 40.375 \n",
       "Q 26.375 40.375 22.484375 35.828125 \n",
       "Q 18.609375 31.296875 18.609375 23.390625 \n",
       "Q 18.609375 15.53125 22.484375 10.953125 \n",
       "Q 26.375 6.390625 33.015625 6.390625 \n",
       "Q 39.65625 6.390625 43.53125 10.953125 \n",
       "Q 47.40625 15.53125 47.40625 23.390625 \n",
       "Q 47.40625 31.296875 43.53125 35.828125 \n",
       "Q 39.65625 40.375 33.015625 40.375 \n",
       "z\n",
       "M 52.59375 71.296875 \n",
       "L 52.59375 62.3125 \n",
       "Q 48.875 64.0625 45.09375 64.984375 \n",
       "Q 41.3125 65.921875 37.59375 65.921875 \n",
       "Q 27.828125 65.921875 22.671875 59.328125 \n",
       "Q 17.53125 52.734375 16.796875 39.40625 \n",
       "Q 19.671875 43.65625 24.015625 45.921875 \n",
       "Q 28.375 48.1875 33.59375 48.1875 \n",
       "Q 44.578125 48.1875 50.953125 41.515625 \n",
       "Q 57.328125 34.859375 57.328125 23.390625 \n",
       "Q 57.328125 12.15625 50.6875 5.359375 \n",
       "Q 44.046875 -1.421875 33.015625 -1.421875 \n",
       "Q 20.359375 -1.421875 13.671875 8.265625 \n",
       "Q 6.984375 17.96875 6.984375 36.375 \n",
       "Q 6.984375 53.65625 15.1875 63.9375 \n",
       "Q 23.390625 74.21875 37.203125 74.21875 \n",
       "Q 40.921875 74.21875 44.703125 73.484375 \n",
       "Q 48.484375 72.75 52.59375 71.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-54\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-54\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_21\">\n",
       "     <g id=\"line2d_37\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"371.958425\" xlink:href=\"#mf53236dc49\" y=\"59.474243\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_31\">\n",
       "      <!-- 0.8 -->\n",
       "      <g transform=\"translate(378.958425 63.273462)scale(0.1 -0.1)\">\n",
       "       <defs>\n",
       "        <path d=\"M 31.78125 34.625 \n",
       "Q 24.75 34.625 20.71875 30.859375 \n",
       "Q 16.703125 27.09375 16.703125 20.515625 \n",
       "Q 16.703125 13.921875 20.71875 10.15625 \n",
       "Q 24.75 6.390625 31.78125 6.390625 \n",
       "Q 38.8125 6.390625 42.859375 10.171875 \n",
       "Q 46.921875 13.96875 46.921875 20.515625 \n",
       "Q 46.921875 27.09375 42.890625 30.859375 \n",
       "Q 38.875 34.625 31.78125 34.625 \n",
       "z\n",
       "M 21.921875 38.8125 \n",
       "Q 15.578125 40.375 12.03125 44.71875 \n",
       "Q 8.5 49.078125 8.5 55.328125 \n",
       "Q 8.5 64.0625 14.71875 69.140625 \n",
       "Q 20.953125 74.21875 31.78125 74.21875 \n",
       "Q 42.671875 74.21875 48.875 69.140625 \n",
       "Q 55.078125 64.0625 55.078125 55.328125 \n",
       "Q 55.078125 49.078125 51.53125 44.71875 \n",
       "Q 48 40.375 41.703125 38.8125 \n",
       "Q 48.828125 37.15625 52.796875 32.3125 \n",
       "Q 56.78125 27.484375 56.78125 20.515625 \n",
       "Q 56.78125 9.90625 50.3125 4.234375 \n",
       "Q 43.84375 -1.421875 31.78125 -1.421875 \n",
       "Q 19.734375 -1.421875 13.25 4.234375 \n",
       "Q 6.78125 9.90625 6.78125 20.515625 \n",
       "Q 6.78125 27.484375 10.78125 32.3125 \n",
       "Q 14.796875 37.15625 21.921875 38.8125 \n",
       "z\n",
       "M 18.3125 54.390625 \n",
       "Q 18.3125 48.734375 21.84375 45.5625 \n",
       "Q 25.390625 42.390625 31.78125 42.390625 \n",
       "Q 38.140625 42.390625 41.71875 45.5625 \n",
       "Q 45.3125 48.734375 45.3125 54.390625 \n",
       "Q 45.3125 60.0625 41.71875 63.234375 \n",
       "Q 38.140625 66.40625 31.78125 66.40625 \n",
       "Q 25.390625 66.40625 21.84375 63.234375 \n",
       "Q 18.3125 60.0625 18.3125 54.390625 \n",
       "z\n",
       "\" id=\"DejaVuSans-56\"/>\n",
       "       </defs>\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-56\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_43\">\n",
       "    <path d=\"M 366.250625 155.361622 \n",
       "L 366.250625 154.9157 \n",
       "L 366.250625 41.651544 \n",
       "L 366.250625 41.205622 \n",
       "L 371.958425 41.205622 \n",
       "L 371.958425 41.651544 \n",
       "L 371.958425 154.9157 \n",
       "L 371.958425 155.361622 \n",
       "z\n",
       "\" style=\"fill:none;stroke:#000000;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p3f5bfbd1de\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"34.240625\" y=\"26.015401\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pc347013f1f\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"115.757147\" y=\"26.015401\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"padfb59dc68\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"197.273668\" y=\"26.015401\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pce7eab1a31\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"278.79019\" y=\"26.015401\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pb75e23d778\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"34.240625\" y=\"129.793583\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p56431db50b\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"115.757147\" y=\"129.793583\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p6457d19a6d\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"197.273668\" y=\"129.793583\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p0bd0da9809\">\n",
       "   <rect height=\"40.758261\" width=\"67.930435\" x=\"278.79019\" y=\"129.793583\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"p2d197f1df0\">\n",
       "   <rect height=\"114.156\" width=\"5.7078\" x=\"366.250625\" y=\"41.205622\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 504x252 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "d2l.show_heatmaps(\n",
    "    dec_inter_attention_weights, xlabel='Key positions',\n",
    "    ylabel='Query positions', titles=['Head %d' % i for i in range(1, 5)],\n",
    "    figsize=(7, 3.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 72
   },
   "source": [
    "尽管transformer架构是为了“序列到序列”的学习而提出的，但正如我们将在本书后面提及的那样，transformer编码器或transformer解码器通常被单独用于不同的深度学习任务中。\n",
    "\n",
    "## 小结\n",
    "\n",
    "* transformer是编码器－解码器架构的一个实践，尽管在实际情况中编码器或解码器可以单独使用。\n",
    "* 在transformer中，多头自注意力用于表示输入序列和输出序列，不过解码器必须通过掩蔽机制来保留自回归属性。\n",
    "* transformer中的残差连接和层规范化是训练非常深度模型的重要工具。\n",
    "* transformer模型中基于位置的前馈网络使用同一个多层感知机，作用是对所有序列位置的表示进行转换。\n",
    "\n",
    "## 练习\n",
    "\n",
    "1. 在实验中训练更深的transformer将如何影响训练速度和翻译效果？\n",
    "1. 在transformer中使用加性注意力取代缩放点积注意力是不是个好办法？为什么？\n",
    "1. 对于语言模型，我们应该使用transformer的编码器还是解码器，或者两者都用？如何设计？\n",
    "1. 如果输入序列很长，transformer会面临什么挑战？为什么？\n",
    "1. 如何提高transformer的计算速度和内存使用效率？提示：可以参考论文 :cite:`Tay.Dehghani.Bahri.ea.2020`。\n",
    "1. 如果不使用卷积神经网络，如何设计基于transformer模型的图像分类任务？提示：可以参考Vision Transformer :cite:`Dosovitskiy.Beyer.Kolesnikov.ea.2021`。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "origin_pos": 74,
    "tab": [
     "pytorch"
    ]
   },
   "source": [
    "[Discussions](https://discuss.d2l.ai/t/5756)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
